Hydrogen Atom Decay in y-Irradiated Sulfuric Acid Glasses
It seems, therefore, reasonable to consider, in addition to the hydrophobic interactions, other forces which could explain the observed results. To explain the extraordinary stability of the p-nitrophenol-CD, one can postulate that in this case the hydroxyl group is in a position where it can most effectively interact with the cyclohexaamylose molecule, probably with one of its secondary hydroxyl groups (via hydrogen bonding) on the rim of the cavity and thus contribute to the stability of the p-nitrophenol-CD. Such an interaction does not seem to be possible if the hydroxyl group is in the meta position to the nitro group. In this case it is supposedly located inside the cavity and cannot interact with the host molecule’s hydroxyl groups on the rim of the cavity. Besides this geometric argument one could consider the acidity constants K , for p- and m-nitrophenol, 690 X and 50 X 10-lo,respectively, as a measure of their relative tendency to undergo hydrogen bonding. These data would clearly indicate a strong preference for the p-nitrophenol to interact via hydrogen bonding with the host molecule as compared to m-nitrophenol. This would be also in line with the fact that the CD complexes of p- and m-nitrobenzoic acid, which have almost the same acidity constants, K , = 36 X and 32 X show identical stabilities (Table I). By the same token, one would have to assume that for geometric reasons the primary hydroxyl groups of the nitrobenzyl alcohols (meta and para), being too far outside the cavity and certainly less reactive than the phenolic hydroxyl, can contribute only very little to the stability of the complex. Whether or not the extra stability of, e.g., the pnitrophenol-CD complex is indeed accomplished via hydrogen bonding cannot be clearly established. The increase in the acidity constants is of course a consequence of differences in the electronic charge distribution in these isomeric molecules, leading also to variations in the dipole moment and polarizability of these molecules. These latter parameters are responsible for the strength of van der Waals-London dispersion forces and the observed differences in complex stability may therefore reflect the contribution of London dispersion forces to the overall binding energy. London dispersion forces were recently suggested by Bergeron et ala4to explain the drastic increase in the stability of CD complexes on going from p-nitrophenol to p-nitrophenolate as guest molecule.
The Journal of Physical Chemistry, Vol. 83, No. 14, 7979
1007
While the results observed with these para- and meta-substituted aromatic compounds, containing polar substituents, clearly suggest the importance of contributions made by hydrogen bonding and/or intermolecular interaction via London dispersion forces to the overall binding energy, the drastic decrease in the stability of CD complexes with o-nitrophenol and o-nitrobenzyl alcohol, in which case K , drops to 8 and 9, respectively, appears to be mostly due to steric hindrance. In addition to the geometric restrictions in the case of o-nitrophenol, the binding capability might be further reduced due to an inactivation of the nitro and hydroxyl group by intramolecular hydrogen bonding between these two groups.
References and Notes This research was supported under Contract No. EY-76-S-05-3602 with the U.S. Department of Energy. For recent reviews on inclusion compound, see, e.g.: (a) Bergeron, R. J. J. Chem. Ed. 1977, 5 4 , 204. (b) Griffiths, D.W.; Bender, M. L. Adv. Cafal. 1973, 209-261. Manor, P.C.; Saenger, W. J. Am. Chem. SOC.1974, 96,3690. Bergeron, R. J.; Channing, M. A.; Giberly, G. J.; Pillor, D. M. J. Am. Chem. SOC. 1977, 90, 5146. Schlenk, H.; Sand, D. M. J . Am. Chem. SOC.1961, 83, 2312. Cramer, F.; Saenger, W.; Spatz, H.-Ch. J. Am. Chem. SOC. 1967, 89, 14; see also previous papers In thls series. Van Etten, R. L.; Sebastian, J. F.; Clowes, G. A.; Bender, M. L. J . Am. Chem. SOC. 1967, 89,3242, 3253. Wood, D. J.; Hruska, F. E.; Saenger, W. J. Am. Chem. SOC.1977, 99, 1735. For general references, see: (a) Green, J.; Lee, J. “Positronium Chemistry”, Academic Press: New York, 1964. (b) Goldanskii, V. I. At. Energy Rev. 1968, 6 , 3. (c) McGervey, J. D. in “Posltron Annihilation”, Steward, A. T.; Roellig, L. 0. Ed.; Academic Press: New York, 1967; p 143. (d) Merrigan, J. A.; Tao, S. J.; Green, J. H. “Physical Methods of Chemistry”, Vol. I, Part 111, Weissberger, A.; Rossiter, B. W. Ed.; Wiley: New York, 1972. (e) Ache, H. J. Angew. Chem., Int. Ed. E@. 1972, 71, 179. (f) Green, J. H. MrPInt. Rev. Sci. 1972, 8 , 251. (9) Goldanskii, V. I.; Virsov, V. G.; Annu. Rev. Phys. Chem. 1971, 22, 209. For Ps-molecule complex formation, see, e.g.: Madia, W. J.; Nichols, A. L.; Ache, H. J. J. Am. Chem. SOC. 1975, 97,5041, where also additional references can be found. Jean, Y-C.; Ache, H. J. J . Phys. Chem. 1976, 80, 1693. Jean, Y-C.; Ache, H. J. J . Am. Chem. SOC. 1977, 99, 1623. Jansen, P.; EMrup, M.; SkytleJensen, B.; Mogensen, 0. Chem. Phys. Lett. 1975, IO, 303. Levay, 8.; Hautojarvl, P. J . Phys. Chem. 1972, 76,1951. Jean, Y-C.; Ache, H. J. J . Phys. Chem. 1977, 87, 2093. Williams, T. L.; Ache, H. J. J . Chem. Phys. 1969 50, 4493. PAL ISa version of the CLSQ nuclear decay analysis program (J. B. Cummings, BNL report 6470), modified by A. L. Nichols In thls laboratory. Casu, 8.; Rava, L. Ric. Sci. 1966, 36, 733.
Kinetics of Trap-Limited Hydrogen Atom Decay in y-Irradiated Sulfuric Acid Glasses Andrzej Ptonka, * Jerzy Kroh, Wrodzimierz Lefik, and Wodzimlerr Bogus Institute of Applied Radiation Chemistry, Technical University of Lddi, 93-590 L6d.2, Wrdblewskiego 15, Poland (Received January 15, 1979)
Using time-dependent rate constants of the form k ( t ) = Bta-l, 0 < 01 < 1,one can describe adequately the complex decay patterns of trapped hydrogen atoms in sulfuric acid glasses with and without 2-propanol added.
Introduction The hydrogen atoms, one of the simplest and most reactive intermediates of radiolytic processes, can be trapped following y irradiation of various oxyacid ices at 77 K.l The trapped hydrogen atoms decay slowly at 77 K. The rate of decay can be speeded up by increasing the temperature above 77 K and/or by adding reactive solutes. 0022-3654/79/2083- 1807$01.OO/O
In all these cases complex decay patterns with evidently time-dependent rate constants are o b s e r ~ e d .So ~ ~far, ~ however, there are no kinetics adquate to describe the trap-limited behavior of hydrogen atom^.^-^ The decay kinetics of trapped hydrogen atoms is controlled by environmental i n t e r a ~ t i o n . The ~ , ~ environment of trapped hydrogen atoms depends upon the irradiation 0 1979 American Chemical Society
1808
Plonka et al.
The Journal of Physical Chemistry, Vol. 83,NO. 14, 1979 In t h i n 1
temperature a t which the hydrogen atoms were formed7 and changes with time at a given temperatures4 Because of that simple classical diffusion kinetics, leading to a time-dependent rate constant, is not adequate for description of hydrogen atom decay reactions. This does not imply, however, that the concept of "diffusive motion" is not applicable. Simple classical diffusion kinetics is based on an exponential distribution function for the jump time leading to a master equation with a constant transition rate between nearest neighbor^.^ The fluctuating jump distances and trap depths in the amorphous systems we are dealing with are reflected by the highly nonexponential distribution function for the jump time in Scher-Montroll model.1° From the long-tail hopping time distribution of this model Hamill and Funabashill derived a time-dependent rate constant of the form
k ( t ) = Bta-1
where 0 < cy < 1. In the following we present evidence that by using time-dependent rate constants of the form given by expression 1it is possible to describe adequately the complex decay patterns of trapped hydrogen atoms in sulfuric acid glasses with and without 2-propanol added. Experimental Section Solutions were prepared from reagent grade sulfuric acid (95 w t %), 2-propanol, and twice distilled water. The acid glass samples, obtained by dropping the solutions into liquid nitrogen, were irradiated with co-60 y rays (1h at a dose rate of 0.7 Mrd/h) at liquid nitrogen temperature. The irradiated samples were transferred quickly into the standard ESR dewar (S-819, Scanco, USA) filled with liquid nitrogen or argon and the ESR spectra of trapped hydrogen atoms were recorded with the use of a X-band type microwave spectrometer (SE-X/20, Poland) equipped with a dual-sample cavity TElo4. A sample of the DPPH-sodium chloride mixture placed as a standard in the reference cavity a t room temperature enabled the corrections of spectrometer operation conditions during prolonged experiments. The reaction time at 77 K was measured from the end of y irradiation while the reaction time at 87 K was measured from the moment of sample immersion into liquid argon. The radiation yield of trapped hydrogen atoms in 6 M sulfuric acid glass y irradiated at 77 K, G(H) = 1.33," was used t o recalculate the relative contents of trapped hydrogen atoms in various samples. Results a n d Discussion The decays of trapped hydrogen atoms at 77 and 87 K in 6 M sulfuric acid glasses y irradiated at 77 K are presented in Figure 1. These decays are due almost exclusively3 to the recombination H+H-+Hz which we describe by the kinetic equation -d[H]/dt = k(t)[H]'
(2) (3)
1.
Introducing eq 1 into eq 3 and integrating within the indicated limits d[H]/[H12 = BLtt"-' dt
15/00 min
Figure 1. Decay of trapped hydrogen atoms at 77 (0)and 87 (0) K in 6 M sulfuric acid glass, y irradiated at 77 K. Details are given in the text.
TABLE I: Kinetic Constants for Trapped Hydrogen Atom Decay in 6 M Sulfuric Acid Glasses with and without 2-Provanol Added additive T,K [HI/ oi Ab BC none none 1.0 M 2-Pr 1.0 M 2-Pr 0.1 M 2-Pr 0.1 M 2-Pr a
77 87 77 87 77 87
(spin/g)lo-".
0.39 0.49 0.38 0.49 0.38 0.49
5.8 6.3 1.1 0.34 4.8 3.6 b
min-".
2.78 6.07 0.094 0.217 0.030 0.080
(g/spin min-a)1020.
Relation 5 yields a straight line in the coordinate system In (([H],/[H] - 1)vs. In t (eq 6). To make use of relation In {([HIo/[HI)- 1)= In (B[HIo/d
+ a In t
(6)
6 it is necessary, however, to have the numerical value of [HI, which is not accessible experimentally. Because of that the numerical values of cy and B, as well as the numerical value of [HIo,were calculated from the minimum of the function (7) where [HI, denotes the concentration of trapped hydrogen atoms measured at time ti and [HI, the respective numerical value from eq 5 . The calculated values of a, B, and [HIo are given in Table I, and in Figure 1 the experimental data plotted according to relation 6 are also shown. It is evident that the experimental data fit relation 6 perfe~t1y.l~ In the presence of 2-propanol the trapped hydrogen atoms decay due to reactions6 2 and H + HC(CH3)ZOH Hz + *C(CH3)20H (8) -+
with the time-dependent rate constant, h(t), given by eq
-GI
1doo
0
(1)
(4)
and the proper kinetic equation is -d[H]/dt = k(t)[H]'
+ k'(t)[H][HC(CH3)2OH]
(9)
Taking k ( t ) and hit) in the form given by relation 1and denoting A = B7HC(CH3),OH], we obtain the relation -d[H]/dt
B[HI2t"-l + A[H]t"-'
(10)
valid for all cases when [HC(CH,),OH] 1 [HI. The use of one numerical value of cy is proved below experimentally. Integration of (10) leads to In ((1/[HI
+ B/A)/(1/[Hlo + B/A)J
= At"/a
(11)
The Journal of Physical Chemistry, Vol. 83,
Hydrogen Atom Decay in y-Irradiated Sulfuric Acid Glasses
0
1
2
I
I
in t jrnin) 3 L I
5
6
7
0
8
I
1
2
3
In t Irninl 4
I
I
1
0
zdo
100
560
Relation 11 simplifies substantially when the contribution of reaction 2 in the decay is negligible in comparison with reaction 8. For B/A 0 we have, from 11 +
In ([Hlo/[HI) = Ata/a
(12)
We have assumed relation 12 to be proper for the description of the decay of trapped hydrogen atoms in the presence of 1M 2-propanol. Relation 12 leads to a straight line in the coordinate system In In ([Hl0/[H])vs. In t (eq 13). As before, because [HI, is not accessible experiIn In ([H],/[H]) = In (A/a) + CY In t (13)
A, and [HI, were mentally, the numerical values of CY, calculated numerically from the minumum of the function i=l
6
7
,
1979
1809
8
,
/
min
Figure 2. Decay of trapped hydrogen atoms at 77 (0)and 87 (0) K in 6 M sulfuric acid glass containing 1 M 2-propanol, y irradiated at 77 K. Details are given in the text.
F(a,A,[HIo) =
5
No. 14,
([Hli/[filJ12
(14)
where [HI, denotes the numerical value given by (13) for ti. The obtained numerical values of CY,A, and [HIo are included in Table I and in Figure 2 the experimental data plotted according to relation 13 are shown. Again a perfect fit13 of the experimental data to relation 13 is evident. Furthermore, the use of one numerical value of CY in eq 10 is justified. The contribution of reaction 2 in this case, estimated from B[H],/(A B[H],), is not greater than 3% a t 77 K and 1%a t 87 K. The constancy of the numerical value of CY for reactions a t a given temperature encouraged us to use relation 11 to describe the decay of trapped hydrogen atoms in the presence of smaller amounts of 2-propanol, i.e., when both reactions 2 and 8 contribute to the decay but [HC(CHJ20H] I [HI holds. Taking the numerical values of CY and B from the above discussed experiments, we have calculated the numerical values of A and [HI, from the minimum of the function
+
F(A,[HIo) = ?{(f([Hl,) - f([fiIJ)/(f([filJ - f([HIo))l2 1=1
(15) where f([HI) = In (l/[HI + B/A) (16) and [H]i denotes the numerical value given by (11)for ti. The obtained numerical values of A and [HI, for the decay of trapped hydrogen atoms in the presence of 0.1 M 2propanol are given in Table I and the experimental data, plotted according to relation 11, are shown in Figure 3.
Figure 3. Decay of trapped hydrogen atoms at 77 (0)and 87 (0) K in 6 M sulfuric acid glass containing 0.1 M 2-propanol, y irradiated at 77 K. Details in the text.
The experimental data fit well13 to relation 11. The coitribution of hydrogen atom recombination to the decay observed in the presence of 0.1 M 2-propanol is equal to about 30% at 77 K and 22% a t 87 K as estimated from the ratio of B[H],/(A + B[Hl0).l4 After looking at the numerical values presented in Table I, two points are worth mentioning. The first point is that the numerical values of CY,0.38-0.39 at 77 K and 0.49 a t 87 K, are not too different from 0.5 to discredit the previously reported curve-fitting results in the coordinate systems3 [H],/[H] or In [H]/[H], vs. 0r15 vs. (-at However, the classical diffusion kinetics leading to these relations is not adequate, as pointed out in the Introduction, to the trap-limited kinetic behavior of hydrogen atoms, and the goodness of fit is reasonable only for decays in short, limited intervals. The second point is that the temperature dependence of the decay patterns is contained in A or B and is related to the detail of environmental interaction on trapped hydrogen atoms and structure of amorphous materials. Here a more detailed explanation of temperature effects is clearly neededll before one attempts to deduce any kind of activation energy. Nevertheless, the apparent activation energies, as estimated from the numerical values of the instantaneous rate constants shortly after exposures to y rays, equal to about 2 kcal/mol, are not only close to those reported previously from our laboratory,’ 2.2-2.3 kcal/mol, but are also in good agreement with the value assigned in the bond excitation model proposed by Angell,le 1.9 kcal/mol. This model easily explains our findings: namely, that the hydrogen atom seems to be released from the traps due to the relaxation processes proceeding in the frozen matrices and because of that the kinetic behavior is interpreted as a redistribution of hydrogen atoms into more and more stable traps proceeding in competition with irreversible decay in reactions with other reactive species present in the matrix. References and Notes (1) R. Livingston, H. Zeldes, and E. H. Taylor, Dlscuss. Faraday Soc., 19, 166 (1955). (2) L. Kevan, “Radiation Chemistry of Frozen Aqueous Solutions” in “Radiation Chemistry of Aqueous Systems”, G. Stein, Ed., The Weizmann Science Press of Israel, Jerusalem, 1968. (3) K. Vacek, Frcg. Probl. Contemp. Radiat. Chem., Roc. Czech. Ann. Meet. Radiaf. Chem., loth, 1970, 367 (1971). (4) E. D. Sprague and D. Schulte-Frohlinde, J . Phys. Chem., 7 7 , 1222 (1973).
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The Journal of Physical Chemistry, Vol. 83, No. 14, 1979
A. K. Galwey and W. J. Hood
(5) L. Kevan and A. Ptonka, J. Phys. Chem., 81, 963 (1977). (6) A. Pbnka, J. Kroh, and K. Wyszywacz, Radiochim. Radioanal. Lett., in press. (7) J. Kroh and A. Wonka, J . Phys. Chem., 79, 2600 (1975). (8) From recent studies of the decay of hydrogen atoms in y-irradiated 6 M sulfuric acid glasses the following picture was inferred. Immediately after irradiation almost all hydrogen atoms are located in shallow4 or unstable7 traps which are present in relatively large numbers. Then the hydrogen atoms move from trap to trap through the matrix until they encounter some reactive species with which they react and disappear or until they encounter a relatlvely deep4 or rather stable7trap from which they are not able to escape quickly. This type of hydrogen motion is to be meant here.
W. H. Helman and K. Funabashi, J. Chem. Phys., 66, 5790 (1977). H. Scher and E. W. Montroll, Phys. Rev. B, 12, 2455 (1975). W. H. Hamill and K. Funabashi, Phys. Rev. B , 16, 5523 (1977). R. Livingston and A. J. Weinberger, J . Chem. Phys., 33, 499 (1960). The 99% confidence limits for the numerical values of a, E , and [H], obtained from (7), for the numerical values of a , A , and [HIo from (14), and the numerical values of A and [HIo from (15) were estimated to be equal to the quoted values 1 1 0 % . (14) The pseudo-first-orderrate constant is not linear with the concentration This phenomenon of 2-propanol as required by A = B'[H'JCH,),OH]. was observed earlier and explained by association in ref 3. (15) K. Ohno, T. Itoh, and J. Sohma, private communication. (16) C. A. Angell, J. Phys. Chem., 75, 3698 (1971). (9) 10) 11) 12) 13)
Thermal Decomposition of Sodium Carbonate Perhydrate in the Solid State Andrew Knox Galwey" and Wllllam John Hood Department of Chemistry, The Queen's University of Belfast, Belfast BT9 5AG, Northern Ireland (Received October 10, 1978; Revised Manuscript Received March 21, 1979)
-
On heating sodium carbonate perhydrate under vacuum, 360-410 K, the constituent hydrogen peroxide decomposed as follows: NazCO3.1.5HzO2 NaZCO3+ 1.5Hz0 + 0.750z. Fractional decomposition (a)-time curves were sigmoid shaped. The reaction rate in 20 torr water vapor was appreciably less than that under vacuum, behavior which markedly contrasts with the large increase in rate found when liquid water was present. It is concluded that the water accelerates the solid state reaction and escape of this product is opposed by the presence of an effective barrier phase of anhydrous Na2C03product. When water vapor was available the residual product was reorganized and the opening of channels permitted the escape of water, with a consequent reduction in the overall reaction rate. -+
Kinetics and mechanisms of thermal decomposition reactions of solids have often been classified1on the basis of two different types of behavior. The rate processes of one class are irreversible and sometimes exothermic, as exemplified by the pyrolyses of azides, permanganates, and perchlorates. In contrast, reactions of the alternative group are reversible dissociations which are frequently endothermic, including, for example, the release of water from many hydrates and of carbon dioxide from carbonates. Kinetic characteristics of reactions in the second class show features which are not found in those of the former, significant differences being that reported activation energies for salt breakdown are often close to the value of the enthalpy of dissociation and the occurrence of Smith-Topley behavior (a specific form of the dependence of reaction rate on the prevailing pressure of product, notably water, in the vicinity of the reactant, see Figures 1 and 2, also pp 213-215, in Chapter 8 of ref 1). Not all solid state decompositions can be correctly assigned to one or other of these two classes, and the present report is concerned with a reaction which incorporates features characteristic of both types, the pyrolysis of sodium carbonate perhydrate, Na2C03.1.5H202. (This salt will be referred to below by the convenient and widely used, though incorrect, name, sodium percarbonate.) The entity which undergoes exothermic and irreversible breakdown on heating, hydrogen peroxide of crystallization, is present in the reactant in a structure from which it may (at least, in principle) be released unchanged by a process analogous to water evolution from crystalline hydrates, reactions already cited as being typical reversible and endothermic dissociations. The results obtained in the present study indicate that during decomposition of sodium percarbonate under vacuum or in water vapor the 0022-3654f 7912083-1810$01 .OO/O
hydrogen peroxide undergoes breakdown within the crystalline reactant. The mechanism operating is, however, quite different from that believed to operate when small, indeed trace amounts of liquid water, are present, since this additive exhibits a pronounced catalytic effect, increasing the rate of product formation and profoundly modifying the kinetic characteristics. Reactions occurring in the presence of liquid water will be more fully described and discussed in a future article. The preparations, structures, and compositions of sodium carbonate perhydrates have been reported by Makarov and Chamova2 and by Firsova et aL3 The thermal decomposition of sodium percarbonate has been described4 as proceeding through three successive stages involving different kinetic obediences. Salts related to the present reactant, for which thermal decomposition studies have been reported, include sodium and potassium peroxocarbonate^,^ K2C03*3H202,6 Rb2C03.3H202,' and Cs&03~3H202.~ Experimental Section Reactants. Sodium percarbonate samples L1, L2, and L3(Fe) were prepared2p3t8in the laboratory by the addition of excess hydrogen peroxide (86% Laporte stabilized) to saturated aqueous sodium bicarbonate (Analar) at ambient temperature. After 30 min of stirring, absolute ethanol was added and the white precipitate of needle-shaped crystals filtered. This product was washed with absolute ethanol, dried overnight, and protected from light during storage. Preparations L1, L2, and L3(Fe) contained 15.0, 14.6, and 13.9 f 0.2% available oxygen, respectively, determined by KMnO, titration. Heavy metal impurities were
