J. Phys. Chem. 1985,89, 3552-3555
3552
VO in an argon matrix are slightly above their gas-phase values. For T i 0 the value of 1005 cm-’ in a neon matrix is also above the gas-phase v a 1 ~ e s . lThe ~ opposite shift is observed for most diatomic molecules as might be expected due to partial solvation of the molecule by the matrix. A shift to higher frequencies suggests that some internal bonding changes other than simple solvation are induced by the matrix. Formation of the H$e(OH)2, H,Ti(OH)z, and H,V(OH)2 species must result from the reaction of one metal atom with two water molecules. This reaction was complete upon cocondensation since no additional product was formed as a result of photolysis; however, there is no evidence to distinguish between a sequential or concerted reaction. Formation of Ti(OH), where x 2 3 is surprising since it indicates facile reaction with three or more water molecules. Reaction with a trimer or tetramer of water seems most likely, but a series of reaction steps is possible. The following equations summarize the reactions observed for atomic Sc, Ti, and V with water in solid argon.
IS K
M + H @ , r
M t 2H20
15 K 7
Ti t n t i g
CM*OH21*
CM*(OH2)23*
IS K 7 HMOH
-
*,
MO t Hz
H,M(OH)2
-
CTi*(OHz),?
Ti(OH),,
n_>3
The asterisk denotes “not observed”, Acknowledgment. The authors are pleased to acknowledge the financial support of this work by the National Science Foundation and by the Robert A. Welch Foundation. Registry No. H20, 7732-18-5; ScO, 12059-91-5;ScOD, 96759-94-3; TiO, 12137-20-1; HTiOH, 81514-91-2; VO, 12035-98-2; V(OH),, 39096-97-4; HSCOH,75594-09-1;HVOH, 81514-92-3;H2180, 1431442-2; DzO, 7789-20-0; Ti(OH),, 12026-77-6; Ti(OH),, 20338-08-3; TiHx, 11 140-68-4;Sc, 7440-20-2; Ti, 7440-32-6; V, 7440-62-2.
Determination of Proton-Transfer Rates and Energetics for the Clathrate Hydrate of Oxirane by FT- I R Spectroscopy Hugh H. Richardson, Paul J. Wooldridge, and J. Paul Devlin* Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078 (Received: February 20, 1985)
The FT-IR spectroscopic observation of proton-transfer rates has been extended to the structure I clathrate hydrate of oxirane. Methods have been developed for isolating DzO intact in the crystalline clathrate at 100 K. Kinetic data for the 105-120 K range indicate direct conversion of DzO to isolated HOD, a result that identifies the orientational defect as the majority charge carrier. The small activation energy for this exchange reaction (-5 kcal) has been tentatively related to the difference between the energy required to mobilize protons trapped by the abundant L-defects (- 12.7 kcal) and the activation energy for formation of the L-defects (-7.7 kcal). The surprising abundance of mobile protons at 110 K has been rationalized by invoking ion-defect formation and trapping during the epitaxial growth of the clathrate samples. Radiolysis effects (1.7-MeV electrons) have added to the understanding of defect behavior in the oxirane clathrate and have permitted the observation of a distinct spectrum for neighbor-coupled (HOD)z units.
-
Introduction The spectroscopic determination of proton-transfer rates for cubic ice has recently provided molecular-level insights to a process that had previously been extensively investigated only by more classical bulk techniques such as conductivity and dielectric constant measurements.’ These new results have been possible because of the development of methods for preparing crystalline cubic ice, at 125 K,containing isolated intact D 2 0 molecules as part of the H-bonded ice network. A kinetic study of the formation of neighbor coupled HOD units, (HOD)2, and isolated HOD from the isolated DzOfor the temperature range from 135 to 150 K yielded quantitative values for the activation energy of proton hopping (9.5 kcal) and orientation defect migration (12.0 kcal) as well as several instructive qualitative insights. Among the latter perhaps the most interesting were firm evidence that (a) the mobility of the hydroxide ion in cubic ice is several orders of magnitude less than that of the proton and (b) the ion pair defects and the Bjerrum orientational defects are comparably effective charge carriers for the temperature range near 150 K. Similar methods have more recently been developed for the isolation of DzO molecules in the H-bonded network of certain crystalline clathrate hydrates so that a similar kinetic study of these substances is possible.2 It is well-known that the host
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(1) W. B. Collier, G. Ritzhaupt, and J. P. Devlin, J. Phys. Chem. 88, 363 (1984).
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water-network structure for the clathrates is icelike in many respects with the average H-bond only 1 .O% longer (weaker) than for ice.3 However, the orientational relaxation rates of the host lattice, which varies somewhat depending on the clathrate guest species, tends to be orders of magnitude greater than for cubic ice.4 Based on the somewhat weaker H bonds and the greater orientational relaxation rates, it is reasonable to anticipate significant differences in results for the thermally induced conversion of the isolated D 2 0 molecules to (HOD)2 and HODimlatd, for the clathrates, compared to the published results for ice. Proton transfer through an H-bonded system apparently occurs by the alternate ”hopping” of a proton ion defect and the passage of an orientational (Bjerrum) L-defect. The hopping step is believed to resemble a small-polaron motion5,6and occurs with a relatively small activation energy that may be positive or negative depending on the temperature in question. Thus the hopping rate, and the associated activation energy, reflects primarily the (2) J. E. Bertie and J. P. Devlin, J. Chem. Phys., 78, 6340 (1983). (3) D. W. Davidson, “Water, A Comprehensive Treatise”, Vol. 2, F. Franks, Ed., Plenum Press, New York, 1973, Chapter 2. (4) D. W. Davidson, S.K. Garg, S. R. Gough, R. E. Hawkins, and J. A. Ripmeester, “Inclusion Compounds”, Vol. 11, Eric Davies, Ed., Academic Press, in press. ( 5 ) M. Kunst and J. M. Warman, J. Phys. Chem., 87, 4093 (1983). (6) K. Kawabata, Y. Nagata, S. Okabe, N. Kimura, K. Tsumari, M. Kawanishi, G. V. Buxton, and G. A. Salmon, J . Chem. Phys., 77,3884 (1982).
0022-3654/85/2089-3552$01.50/00 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 16, 1985 3553
Clathrate Hydrate of Oxirane equilibrium number of proton ion defects, which, for pure ice, becomes vanishingly small at T < 135 K. The larger L-defectmigration activation energy (13.2 kcal)' is usually regarded as a composite of the formation and mobilization energies, although this viewpoint has recently been ~hallenged.~ Crystalline ice may very well be unique in the sense that the rates of the two steps, proton hopping, capable of converting isolated D 2 0 to (HOD),, and L-defect passage, required for the separation of (HOD), into isolated HOD units, are essentially identical for the temperature range corresponding to laboratory-time-scale half-lives (i.e., 0.1 to 10.0 h). Since the hopping rate depends on H 3 0 + ,which might be expected to be reduced for the more weakly H-bonded clathrates, while rapid L-defect migration is reflected in the much greater orientational-relaxation rates of the clathrates, it follows that, in contrast to the situation for ice, the hopping rates should be orders of magnitude less than the L-defect-passage rate for the clathrates. In terms of the two basic proton exchange steps D20+ H20 (HOD),
k2
ki
(HOD),
2HODi,,
(hopping)
(L-defect passage)
it is thus expected that k2 >> kl so that the hopping step alone should be rate controlling and the concentration of (HOD)2 should be so low as to escape spectroscopic detection throughout the exchange reaction. Further, since no exchange occurs without proton hopping, one might project that, unless the guest clathrate species is an intrinsic source of mobile protons, the overall proton exchange rates for the clathrates should be less than for crystalline cubic ice at comparable temperatures. Since methods have been developed for isolation of D 2 0 in the crystalline clathrate of oxirane (ethylene oxide), it is now possible to report the results of a kinetic study of thermally induced proton migration in this crystalline clathrate. Further, data obtained for samples containing an artificially high concentration of protons, generated by electron bombardment (1.7 MeV), will be shown to complement the results of the thermal study.
Experimental Section The samples of the crystalline clathrate hydrate of oxirane containing intact isolated DzO molecules were prepared by epitaxial growth. An ultrathin oxirane clathrate crystalline film was first formed by annealing an amorphous deposit of the clathrate mixture at 130 K. this film then served as a substrate for growth of the D,O-containing clathrate using separate molecular beams of D 2 0 and a 5:l H20-oxirane mixture which were condensed on the film surface at 100 K, in vacuo, at a rate of 0.2 pm/min. The D20, which was obtained from Merck and Co. Inc. as 99.96% deuterium enriched, was used after degassing in several freezethaw-pump cycles. The H 2 0 was similarly degassed after triple distillation before mixing with the oxirane which was taken directly from a Matheson lecture bottle.8 The kinetics of the thermal proton-exchange reaction were determined for the temperature range from 105 to 120 K corresponding to D 2 0 half-lives varying from -3 h to -10 min. Sample temperatures were established by using an Air Products Displex CS-202 refrigerator and maintained to f 0 . 5 K by a programmed Air Products temperature controller. The infrared spectra were measured as a function of reaction time with a Digilab FTS-20C Fourier transform spectrometer. The reaction temperatures were chosen so that the time to collect a 10-scan interferogram was short compared to the half-life of the isolated D20. The spectral subtract capabilities of the spectrometer were used extensively to reveal, separately, the growth of the HOD band (7) P. V. Hobbs, 'Ice Physics", Oxford University, London, 1974, Chapter 2. (8) Though the series of rate measurements reported in this paper were made with oxirane without further purification, the proton-transfer rates for the oxirane clathrate have been found to be insensitive to both oxirane purification by vacuum-line distillation and change in the lecture-bottle source of the oxirane.
2500
-1 cm
2400
2300
F'igure 1. Infrared absorbance curves (10 K) for (a) D20,(b) HOD*d, and (c) (HOD)z in the 0-D stretching region of the oxirane clathrate hydrate. The (HOD)z absorption was deduced from an irradiated sample.
(vOD) and the diminution of the D 2 0 v 1 and v3 absorption bands.
The effect of 1.7-MeV radiation on the D 2 0 exchange reaction was also observed independent of the thermal kinetics measurements. Thin clathrate films, at 75 and 30 K, were irradiated with 1.7-MeV electrons from a Van de Graff generator at dosage levels in the le1eV/g range. The estimated G values for proton transfer were approximately 20. ReSultS As was noted earlier, the thermal proton-exchange mechanism was expected to consist of a slow hopping step, with formation of (HOD)2, followed by the rapid passage of an L-defect, causing the immediate conversion of (HOD), to isolated HOD. Accordingly, the only deuterated spectroscopic species expected were D 2 0 and isolated HOD. The thermal rate data have been analyzed on this basis which will be shown to be valid by using the radiolysis results. The necessary spectra for HOD and D 2 0 have been previously chara~terized.~Since it is not possible to obtain isolated D 2 0 without some HOD contaminant, the isolated D,O spectrum has been deduced by subtracting a subjectively determined amount of HOD absorption from the original D 2 0 spectrum. Because both the HOD and D 2 0 absorption bands shift significantly with temperature variations of more than a few degrees, the reference HOD and D 2 0 spectra, such as presented for 10 K in Figure 1, were evaluated for each of the temperatures used during the rate studies. Thermal Rate Data. The variation in the v I (2380 cm-I) and u3 (2455 cm-') band intensities of DzO as a function of time at 118 K is displayed in Figure 2. A similar series of bands, for temperatures ranging from 105 to 120 K, have been obtained for seven separate samples. An Arrhenius plot of the first-order rate constants, deduced from the time dependence of the peak heights, is presented in Figure 3. From this plot an activation energy of 5.0 f 1.8 kcal has been estimated for the proton-hopping step for the oxirane clathrate hydrate. Radiation-InducedProton Transfer. The L-defect-passage rate was presumed to be much greater than the thermal proton-hopping rate for the oxirane clathrate since the small activation energy for dielectric relaxation is suggestive of a relative abundance of mobile Ldefects in the clathrate! However, the L-defect to proton ratio can be manipulated, as has been done previously with cubic ice,l0 by electron bombardment at much lower temperatures. The (9) H. H. Richardson, P. J. Woaldridge, and J. P. Devlin, J. Chem. Phys., submitted for publication.
3554
, Richardson et al.
The Journal of Physical Chemistry, Vol. 89, No. 16, 1985
isolated HOD occurred at 90 K. Further, irradiation of fresh samples of the oxirane clathrate a t 70 K was found to convert D 2 0 directly to isolated HOD with no buildup of the (HOD), concentration. With the spectrum of (HOD)2 available from this radiolysis study (curve c, Figure l), it was possible to return to the thermal rate data to search for any contribution by (HOD)2to the observed infrared spectra for various stages of the thermal reaction. The fitting of the observed absorption features in the 0-D stretching region was not improved significantly by including an (HOD)2 component, confirming that D 2 0 and HOD, but not (HOD)2, are important spectroscopic species for the thermal rate study.
2500
2400
2300
“1
Figure 2. Time variation (minutes) in the intensity of the D20stretching mode absorption bands for a kinetic run at 118 K.
Discussion It is clear from the above results that, in some respects, proton migration through the oxirane clathrate hydrate behaves as anticipated whereas other observations are in direct contradiction with expectations. The data do support the view that the ratelimiting factor for proton migration is the low concentration of mobile protons rather than a lack of mobile L-defects as evidenced by the direct conversion of D 2 0 to isolated HOD. Further, the radiolysis results confirm that a significant concentration of mobile L-defects are present at much lower temperatures than for cubic ice, since the conversion of (HOD)2 to HOD is rapid even for temperatures less than 90 K. The corresponding reaction for cubic ice is extremely slow below 120 K.l,lo Finally, the new data confirm that, as for cubic ice, mobile protons can be generated in the clathrate hydrates, in the absence of mobile L-defects, by 1.7-MeV electron bombardment, but only at temperatures much lower than noted for cubic ice (90 K).l0 However, the presence of thermally induced proton hopping at 105 K, 30 K below the onset of proton hopping in cubic ice, was unexpected and might be taken as evidence that the ionization energy of the clathrate is much less than for cubic ice. Even more surprising is the small value determined for the activation energy of proton hopping ( - 5 kcal), approximately one-half the value found for cubic ice in the 140 K range (9.5 kcal). If the observed E, value for proton hopping is applied in the same manner as E, for cubic ice,’,’ the estimated ionization energy for the clathrate hydrate is given as 10 kcal. This is in sharp contrast with the value of 13.4 kcal for liquid water and the estimates for ice in the 17-19-kcal range. If the viewpoint that the ionization energy for the oxirane clathrate hydrate should be comparable to or greater than that for cubic ice is retained, an explanation for the observed rate data must be found. The most obvious possibility, and one that cannot be completely discounted at this time, is that the clathrate hydrate samples may have been contaminated with traces of a weak acid that ionized more readily, and at a lower temperature, than water. However, a more attractive explanation is available that combines several ideas regarding the behavior of defects in H-bonded systems. Warman has s~ggested,~ and some codinnation has been offered,1° that protons form a complex with L-defects in ice with an activation energy for dissociation of ~ 1 2 . 6kcal. Such a complex should be far more important for the clathrate hydrates than for ice since the expected L-defect concentration, for a given temperature, is orders of magnitude greater. However, the complex cannot form in significant quantities without a supply of protons greater than that anticipated at 100 K. One possibility is that the abundance of protons required for the observed thermal rates may be generated in the clathrate water network by the heat of condensation released during the epitaxial growth of the hydrate crystals. Once generated, the excess protons would be trapped by the abundant L-defects, rather than eliminated by recombination with the less abundant OH- ions. Consequently, the protons are present at 100 K but are immobilized by complexation. Warming into the 110 K range releases the trapped protons at a rate determined by the binding energy so that a pseudo-equilibrium develops
-
Figure 3. Arrhenius plot of the rate data for conversion of D20 to HOD,,,I,,d in the oxirane clathrate hydrate.
mobile L-defect population is rapidly reduced as an icelike sample cools while electron bombardment generates solvated electronproton charge pairs regardless of the temperature. For certain combinations of temperature and bombardment rate, the relative rate for hopping and L-defect passage is inverted and, at a sufficiently low temperature, the L-defect passage is completely stopped. Thus, electron bombardment can generate mobile protons in the absence of mobile L-defects so that the deuterated spectroscopic species become D 2 0 and (HOD)2 rather than isolated HOD. Irradiation is seen to provide a means for establishing a significant (HOD)* concentration, the spectrum of which is presented as curve c in Figure 1. In particular, electron bombardment at 30 K ( 1021eV/g) was found to convert -30% of the isolated D 2 0to (HOD)* with little, if any, formation of isolated HOD. Such an irradiated sample was stable to subsequent annealing at temperatures as high as -70 K. However, rapid conversion of the remaining D,O to (HOD), and, ultimately,
-
~
H30+.L ~2 H30++ L
~~
(10) J. P. Devlin and H. H.Richardson, J . Chem. Phys., 81, 3250 (1984).
which controls the proton concentration available for the observed
Clathrate Hydrate of Oxirane thermal proton exchange reaction. This pseudo-equilibrium is strictly analogous to one proposed and used by Warman et al.5 to interpret the slow decay in conductivity following the pulse radiolysis of ice. In that case the “equilibrium” concentration of protons is slowly depleted by recombination with the immobilized solvated electrons whereas in the present instance the ultimate recombination is with the artificially high concentration of immobilized hydroxide ions. From the proposed pseudo-equilibrium, assuming that the concentration of the complex is so large as to be nearly constant throughout the rate measurements, it follows that [H30+] = Ae-(AHD-EaL)/RT= Ae-EJRT where AHDis the complexdissociation energy, E t is the activation energy associated with the L-defect concentration, E, is the observed activation energy for proton hopping, and A is a composite of constants. Recognizing that the L-defect formation energy is 17.7 kcal: and using the experimental E, value of 5.0 kcal, it follows that AHD I 12.7 kcal. This upper limit for AHD is the same value deduced previously from the pulse radiolysis of ice.s The actual value for AHDdepends on the fraction of the 7.5kcal that must be assigned to mobilization of the L-defects. If, as has been suggested for ice,5 this value is quite small, then the MD value deduced for ice and the clathrate hydrate are both approximately 12.5 kcal. If this pseudo-equilibrium model is valid one should expect that the [H30+.L] and, therefore, [H30+]should decay slowly during a kinetic run at a fixed temperature. This would be reflected in a reduced effective rate constant and an increased D 2 0 half-life. The monitoring of the D 2 0 half-life values through the course of the kinetic runs did show that a slow increase occurs (i.e., the average ratio of the second half-lives to the first half-lives was =1.3).” If protons are released during the condensation of a clathrate they must similarly be released during the condensation of ice. However, with fewer L-defects available and with the condensation temperatures used for pure cubic ice (125 K)too great for effective trapping of protons by the L-defects on a laboratory time scale, it is not surprising that such trapping does not figure prominently (1 1 ) If this apparent decay in the mobile proton concentration during the rate measurements is recognized, by using rate data for only the first quarter-life of the exchange reactions, the slope of the line in Figure 3 is slightly enhanced so that an E, value closer to 6.0 than 5.0 kcal is indicated.
The Journal of Physical Chemistry, Vol. 89, No. 16, I985 3555 in the apparent mechanism for conversion of D 2 0 to isolated HOD.’ This suggests that the extra protons realeased in ice must move significant distances to recombine with hydroxide ions as the equilibrium concentrations are established a t the deposition temperature (125 K). Consequently, a fraction of the D 2 0 must inevitably be converted to HOD during the epitaxial growth of cubic ice. Observations in support of this deduction have been made but not reported. Thus, it is clear from previous ice studies that the amount of HOD contained in the H20-D20 deposits at 125K is (a) reduced for base-doped samples and (b) greater for increased deposition rates. Both observations require the presence of a nonequilibrium concentration of protons during the condensation process, since the equilibrium proton concentration at this temperature is trivial (Le., a D 2 0 half-life of several hours).’ Conclusions
It is possible to grow thin films of the crystalline clathrate of oxirane a t 100 K which contain intact isolated D20molecules. Upon warming only slightly, into the 110 K range, the isolated D 2 0 converts directly to isolated HOD units, with no buildup in the concentration of (HOD),, in a manner consistent with a high population of mobile L-defects. However, this conversion also requires a mobile proton concentration, at 110 K,comparable to that found in cubic ice at 140 K. Further, the activation energy for proton hopping deduced for the oxirane clathrate hydrate (-5.0 kcal) is apparently too small to be directly related to the clathrate ionization energy. A pseudo-equilibrium model that combines the concepts of (a) high clathrate L-defect population, (b) ion-pair defect formation during clathrate deposition (via the released heat of condensation of 11.2 kcal/mol), and (c) L-defect shallow-trapping of protons explains the surprising rate data. This model relates the observed activation energy for proton hopping to the difference in the energy required for the proton to escape from an L-defect trap and the energy for formation of L-defects with the result that a maximum value of 12.7kcal is obtained for the energy of dissociation of the proton from the L-defect. Radiolysis studies have confirmed the view, derived from dielectric relaxation studies, that the L-defect concentration for the clathrate hydrate is much greater than for cubic ice at comparable temperatures (as required by the model). Acknowledgment. Support of this research under National Science Foundation Grant CHE-8209702 is gratefully acknowledged. Registry No. Oxirane hydrate, 16002-48-5.
