Jerzy Kroh and Andrzej Wonka
2600
other hand, is reduced owing to the blocking of the growth sites by the presence of adsorbed additive ions. References and Notes
L 1 14
TIME
16
Irnin)
Figure 4. Effectof sodium pyrophosphate on the dissolution of calcium oxalate monohydrate: plots of the integrated form of eq 3: expt 83,0, 0.0 M [ P ~ 0 7 ~ - ]expt ; 8 5 ~A,~ 4.9 , X loy7 M [P2q4--]: expt 8 6 ~ s 0, , 4.2 x M [P2074-].
fitted the dissolution data as shown by the linear plots in Figure 4.In Table 11, the results of some experiments of the rate of growth of seed crystals from stable supersaturated calcium oxalate solutions18 are included for comparison. It can be seen that, at a concentration of [P2074-]= 4.90 X M , the rate constant for dissolution is about 75% of that in the absence of additives. In the corresponding crystal growth process (Table 11), the rate constant was reduced to only 15%of that in the absence of additives. If the pyrophosphate ion is adsorbing at high-energy surface sites or dislocation line sources on the crystal surface, the crystal dissolution process at other surface sites would be unaffected if diffusion control predominates. Crystal growth, on the
E. L. Prlen and E. L. Prien, Jr., Am. J. Med., 45, 654 (1968). A. Chambers, A. Hodgkinson, and G. Hornung, Invest. Urob, 9, 376 (1972). J. MacGregor, W. G. Robertson, and B. E. C. Nordin, Br. J. Urol., 37, 518 (1965). C. Y. C. Pak, E. D. Eanes, and 8. Ruskln, Proc. Nat. Acad. Sci. U.S.A., 68, 1456 (1971). G. H. Nancollas and B. Tomazic, J. Phys. Chem.. 78, 2218 (1974). A. A. Noyes and W. R. Whitney, J. Am. Chem. SOC.,19,930 (1897). W. Nernst, J. Phys. Chem., 8, 52 (1904). S.T. LiuandG. H. Nancollas, J. lnorg. Nucl. Chem., 33, 2311 (1971). A. L. Jones, Trans. Faraday SOC.,59, 2355 (1963). A. L. Jones, H. G. Linge, and I. R. Wilson, J. Cryst. Growth, 12, 201 (1972). J. R. Campbell and G. H. Nancollas, J. Phys. Chem., 73, 1735 (1969). G. H. Nancollas and R. W. Marshall, J. Dent. Res., 50, 1268 (1971). D. W. Bishop, J. D. Eick, G. H. Nancollas, and W. D. White, J. Dent. Res., 53, 198 (1974); IADR Program and Abstracts of Papers, No. 575, 1974. F. Young, M. Fawzi, M. G. Dedhiya, M. S. Wu, and W. I. Higuchi, J. Dent. Res., 53, 198 (1974); IADR Program and Abstracts of Papers, No. 576, 1974. J. F. Desmars and R. Towashi, Biochim. Biophys. Acta, 313, 256 (1973). G. Kallistratos and Y. Hayase, Jpn. J. Urol., 64, 555 (1973). G. Kallistratos, Urd. ht., 29, 93 (1974). G. H. Nancollas and G. L. Gardner, J. Cryst. Growth, 21, 267 (1974). B. Finlayson and A. Smith, J. Chem. Eng. Data, 18, 368 (1973). C. W. Davies, "Ion Association," Butterworth and Co., Ltd., London, 1962. E. A. Moelwyn-Hughes, "The Kinetics of Reactions in Solutions," 2nd ed. Oxford University Press, London, 1947. S. T. Liu and G. H. Nancollas, J. Cryst. Growth, 6, 281 (1970). D. M. S.Little, Ph.D. Thesis, Glasgow University, 1964. D. M. S. Little and G. H. Nancollas, Trans. Faraday SOC., 66, 3103 (1970). K. Lonsdale and D. J. Sutor, Sov. Phys.-Crystallogr. (fngl. Trans.), 16, 1060 (1972). D. J. Sutor and S. E. Wooley, Br. J. Urol., 44, 532 (1972). B. Hodes, Ph.D. Thesis, University of Michigan, 1972. H. Fleisch and R. G. G. Russell, J. Dent. Res., 51, 324 (1972). H. Fleisch and S. Bisaz, Am. J. Physiol., 203, 671 (1962).
Trapped Hydrogen Atom Decay in y-Irradiated Sulfuric Acid Glasses at 63-90 K Jerzy Kroh* and Andrzej Ptonka lnstitute of Applied Radiation Chemistry, Technical University (Politechnika), Wroblewsklego 15,93490tod2, Poland (Received October 21, 1974; Revised Manuscript Received August 15, 1975)
No isotope effect was observed in the decay of trapped hydrogen and deuterium atoms in y-irradiated deuterated 6 M sulfuric acid glasses with 2-propanol added. The trapped hydrogen atoms seem to be released from the traps due to the relaxation processes proceeding in the frozen matrices. Because of that the kinetic behavior is interpreted rather as a redistribution of hydrogen atoms into more and more relaxed traps, than into deeper and deeper traps, proceeding in competition with irreversible decay in reactions with other reactive species present in the matrix.
rntroduction From recent studies1 of the decay of hydrogen atoms in y-irradiated 6 M sulfuric acid glasses the following picture was inferred. Immediately after the irradiation almost all hydrogen atoms are located in shallow traps which are present in relatively large numbers. Then the hydrogen The Journal of Physical Chemistry, Vol. 79, No. 24, 1975
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 relatively deep trap from which they are not able to escape quickly. To accept this picture one is forced to assume that trapped hydrogen atoms are released from virtually intact traps.
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Hydrogen Atom Decay in y-Irradiated H&04 Glasses
There is, however, another possibility, strongly suggested by our findings in alkaline ices,2v3 that the trapped species could be released due to the relaxation processes proceeding in the frozen matrices at low temperatures. To demonstrate this possibility we present below some experimental data.
Experimental Section Reagent grade (95 wt %) sulfuric acid, deuterium oxide, and 2-propanol were used to prepare the deuterated 6 M sulfuric acid containing a varying amount of 2-propanol. The acid glass samples, prepared by dropping these solutions into the liquid nitrogen, were irradiated with co-60 y-rays (1 hr at the dose rate of about 1.3 Mrads/hr) at 63-90 K. The lowest temperature, 63 K, corresponding to the triple point of nitrogen, was achieved in that case by the usual vapor pumping technique. To perform the experiments a t higher temperatures, the irradiation was carried out either in the liquid nitrogen, 77 K, or in the stream of cold nitrogen gas, up to 90 K. The content of trapped hydrogen and deuterium atoms accumulated under the above experimental conditions, as well as their subsequent decay at temperatures 67-90 K, was observed by their ESR spectra recorded with the use of X-band type microwave spectrometer (SE-X/BO,Poland) a t 100-Hz field modulation. To record the ESR spectra the y-irradiated samples were quickly transfered, under liquid nitrogen, into a standard ESR Dewar vessel (S-819, Scanco, USA) into which a stream of helium gas was injected, temperature range 67-77 K, or into the disposible tube fitting a variable temperature insert attached to the ESR microwave cavity. This variable temperature insert was similar to that used for yirradiation and maintained a constant temperature, within the range of 2 O , up to 90 K which corresponds to the highest temperature at which the trapped hydrogen or deuterium atoms can be observed under our experimental conditions. In each case the first ESR spectrum was recorded 15 min after the end of the irradiation and that time was taken as zero of the reaction time.
0
a2
04
08
05
10
[HIt /Pllo
Figure 1. The fraction of remaining trapped deuterium atoms vs. the fraction of remaining trapped hydrogen atoms for the same time periods during the reaction course at 77 K in a matrix irradiated at 77 K, 77/77, at 67 K in a matrix irradiated at 77 K, 77/67, at 77 K in a matrix irradiated at 90 K, 90177, and at 77 K in a matrix irradiated at 63 K, 63/77.
H conci ru
10 A
3
& A 0
o\
0
77167 77177 901 77 901 90
05
Results and Discussion Increasing the concentration of 2-propanol in the deuterated 6 M sulfuric acid glasses above the limit used in the above mentioned investigations,l equal to about 0.07 M , we have found it convenient to execute the experiments at a concentration of about 1.3 M in the temperature range 63-90 K. Under these conditions the absolute concentration of trapped hydrogen and deuterium atoms amounted, as observed immediately after the irradiation by their ESR spectra recorded at low microwave power, to some 10% of the amount observed in the pure 6 M sulfuric acid glass irradiated at 77 K and an appreciable decay was observed in 2-3-hr periods. The trapped hydrogen and deuterium atoms disappeared at the same rates, as it is evident from Figure 1 presenting the fraction of the remaining trapped deuterium atoms vs. the fraction of the remaining trapped hydrogen atoms for the same time instants under various experimental conditions. The lack of an appreciable isotope effect, at all temperatures, can be taken, in our opinion, as evidence that the trapped species are released rather due to matrix relaxation than due to quantum mechanical tunneling from the intact traps. One may assume that both hydrogen and deu-
0
100
200
Re a c ti on time, min
Figure 2. Decay of trapped hydrogen atoms at 67 K in a matrix irrediated at 77 K, 77/67, at 77 K in a matrix irradiated at 77 K, 77/77, at 77 K in a matrix irradiated at 90 K, 90177, at 77 K in a matrix irradiated at 63 K, 63/77, and at 90 K in a matrix irradiated at 90 K, 90/90.
terium atoms are localized in similar traps in the given matrix. Because of large difference in masses the difference in probabilities for escaping by traversing any potential barrier, either classically or quantum mechanically, should be significant while the probabilities for the destruction of a trap containing either hydrogen or deuterium atom should be similar. The Journal of Physical Chemistry, Vo/. 79, No. 24, 1975
Wen Yaung Lee and L. J. S&tsky
2602
The probability for trap destruction due to molecular rearrangement should be lower in a more relaxed matrix containing fewer frozen configurations which are unstable a t the given temperature. The matrix irradiated a t a temperature higher than that of observation is more relaxed, and the matrix irradiated a t a temperature lower than that of observation is less relaxed than that irradiated a t the temperature of ob~ervation.~ Because of this rate of trapped hydrogen atom decay a t the given temperature, e.g., 77 K, cf. Figure 2, regardless the difference in initial yields displayed in the relative units, is greater in the matrix irradiated at 63 K, cf. curve 63/77, and lower in the matrix irradiated a t 90 K, cf. curve 90177, than in the sample irradiated a t 77 K, cf. curve 77/77. Comparing the effect of temperature decrease on the rates of trapped hydrogen atom decay in matrices irradiated a t 77 K, cf. curves 77/77 and 77/67 in Figure 2, and 90 K, cf. curves 90/90 and 90177 in Figure 2, we have estimated nearly equal numerical values of the apparent activation
energy for trapped hydrogen atom decay, 2.3 and 2.2 kcall mol, re~pectively.~ This is consistent with our assumption of trap destruction due to molecular rearrangement which, despite the difference in probability, should proceed with the same apparent activation energy at both temperatures. References a n d Notes (1) E. D. Spraque and D. Schuite-Frohiinde, J. Phys. Chem., 77, 1222 (1973). (2) J. Krohand A. Pionka, Int. J. Radiat. Phys. Chem., 8, 211 (1074). (3) J. Kroh and A. Pionka, Chem. Phys. Lett., 28, 186 (1974). (4) It is worthy to note the importance of irradiation temperature and relative insignificance of preirradiation temperature. It was conclusively shown in ref 1 that, at least with respect to the traps available for hydrogen atoms produced by y-irradiation at 77 K, no changes in th! 8 M H2S04 matrix occurs on warming to 87 K before irradiation. (5) Much greater numerical values, 4.1 and 5.79 kcal/mol, of the apparent activation energy are reported in ref 1 for hydrogen atom decay immediately and 200 hr after the irradiation, respectively. Because of experimental differences it is difficult to compare the numerical data. if, however, there was no great deviation of the decay curve at 87 K from the first-order decay, a much smaller apparent activation energy can be lnferred from the results presented in Figure 3, ref 1.
Heat of Vaporization, Infrared Spectrum, and Lattice Energy of Adamantane W e n Yaung L e e and L. J. Slutsky" Department of Chemistry, University of Washington, Seattle, Washington 98 195 (Received May 27, 1975)
The vapor pressure of adamantane can be expressed as In P,, = 50.27 - (8416/T) - 4.211 In T (2' in OK) between 278 and 443 K. The heat of vaporization at 300 K is 14.210 kcal/mol, the cohesive energy a t 300 K is -15.445 and -15.848 kcallmol at 0 K. Frequency shifts of the infrared-active internal modes of adamantane with temperature and on vaporization are reported.
I. Introduction Adamantane, by virtue of the high (Td) symmetry of the molecule and the simplicity of the crystal structure1 of the high-temperature, cubic close-packed phase, constitutes a simple system in which approaches to the computation of intermolecular forces,2 lattice-dynamical frequency distrib u t i o n ~ , intramolecular ~,~ potential function^,^ thermodynamic properties,6 infrared spectra, and a priori deduction of the crystal structures7 of organic solids can be tested. In all such studies the static lattice energy as deduced from the experimental heat of vaporization and related thermodynamic data enters, either as one of the quantities which determine the parameters of the intermolecular or interatomic potential function or as a critical test of the adequacy of the assumed potential. We wish here to report new results on the heat of vaporization and infrared spectrum of adamantane and to briefly discuss the calculation of the static lattice energy and the parameter of the intermolecular potential function. 11. Results and Calculations The initial purity of the adamantane as specified by the supplier14 was 99+%. Repeated fractional vacuum sublimation did at length give a sample with an equilibrium vapor The Journalof PhysicalChemistry, Vol. 79,No. 24, 1975
pressure invariant upon partial sublimation. The residual pressure in the vacuum system was 2 X lov9 Torr, and the pressure with the adamantane a t liquid nitrogen temperature was 2 X indicating effective removal of any occluded atmospheric gases. The vapor pressure was measured to f0.06% with an MKS capacitance manometer. The temperature regulator was an adaptation of that described by Larsen,15 and the temperature was measured by an NBS calibrated Leeds and Northrup platinum resistance thermometer. The vapor pressure of adamantane as a function of temperature as determined in this work and by Bratton and Szilard? Boyd: and Wu, Hsu, and Dows7 are given in Figure 1,where the solid curve represents a least-squares fit of the results of Boyd, Bratton, and Szilard and the present work to the form In P,, = 50.27 - (8416/T) - 4.211 In T , where T is in O K . The infrared frequencies in the cubic solid at 225 and 298 K and in the vapor are listed in Table I. The heat of vaporization a t 300 K is 14.210 kcal/mol. Within the framework of the quasi-harmonic approximation, the energy of the solid phase a t a temperature T when the lattice parameter is a may be expressed as U ( a ) E o ( a ) + E(a,T),where U ( a )is the potential energy, Eo(a) the zero-point energy, and E(a,T) the thermal vibrational
+
