J. Phys. Chem. 1992, 96, 5658-5662
5658
Alkane Reactions with Photoactivated Decatungstate in Neutral and Acid Solution. Molecular Orbital Theory S.-F.Jen,t Alfred B. Anderson,*,+and Craig L. Hills Chemistry Department, Case Western Reserve University, Cleveland, Ohio 441 06-7078,and Department of Chemistry, Emory University, Atlanta, Georgia 30322 (Received: February 10, 1992)
0- hole centers produced by charge-transfer photoexcitation in WloO324- abstract H from alkanes as do 0- in numerous solid-state and molecular analogues. Upon protonation, forming H2WloOsze,this activity increases, and this has been modeled with atom superpition and electron delocalization molecular orbital (ASED-MO) calculations by shifting the polyoxometalate valence bands by an amount suggested by the observed decrease in first reduction potential. This strengthens the OH bond that forms at the anion surface when an alkane H is abstracted and lowers the activation energy for the process. The calculations show that in the absence of acid the resulting alkyl radicals bind weakly to the polyanions because the binding is reductive, promoting an electron to the empty W 5d band, but electron transfer to this band is possible for secondary and tertiary carbon radicals in the case of Wlo032e, yielding carbocations. In acidic media, the stronger oxidant H2W10032- is likely to be. capable of oxidizing primary carbon radicals and methyl radicals.
Introduction In this paper we develop a theoretical framework for understanding the effects of protonation of the polyoxotungstate anion, WIo032e (Figure l), on photoactivated hydrogen atom abstraction from alkanes.' This anion has an optical absorption peak at 3.80 eV (326 nm) which is attributable principally to charge-transfer excitation between the filled 0 2p and empty W 5d bands. The band edge in the spectrum is about 3.1 eV (400 nm), which represents the band gap. The reaction R-H + WIoO324-- R' + HW10032'~(1) is equivalent to proton transfer to an 02-and electron promotion to the W 5d band. Since the R-H and ChH bond strengths are within a few tenths of an electronvolt of one another and an electron must be promoted over a large band gap, reaction 1 does not go spontaneously. If the polyoxoanion is activated by charge-transfer photoexcitation, creating a hole at the top of the 0 2p band and an electron in the W 5d band, denoted as W100324-*, the reaction can be spontaneous. In this case one is swapping an ChH bond for an R-H bond which is several tenths of an electronvolt weaker: Wl0032~-+ h V Wl0032~-* (2) R' HWlo032*4Wl0O32-* R-H (3) In reaction 3 the electron that comes to the polyanion with the proton is not promoted over the 3.1-eV band gap but instead reduces the relatively low-lying hole on 0-. The hole is, of course, in a molecular orbital that is delocalized over the formal 02-ions that make up the surface of the polyanion, and a stable localized u OH orbital forms when H binds to one of the surface oxygen sites. This process was discussed in a recent theoretical study,2 where it was shown that the R-H u orbital energy level indeed lies beneath the hole level at the top of the 0 2p band. One can anticipate that if the 0 2p band could be made more stable, the stability of the R' + HWlo032.e products would increase and the activation energy calculated in ref 2 might decrease, speeding up the reaction and increasing the quantum yield. The W100324-0 2p band would be stabilized if positive charge could be added. This might be achieved electrochemically by oxidizing the polyanion over an anode surface, but we are unaware of this being attempted. Although considerable documentation is now available on the redox behavior of polyoxometalate complexes as assessed in solution by cyclic voltammetric methods, and oxidation of reduced polyoxometalates is often facile, there is no evidence that the oxidized (do) complexes can be oxidized appreciably under these ~ondition.~A second approach would be
+
-+
+
'Case Western Reserve University. lPresent address: Cleveland Clinic, FFI,9500 Euclid Ave., Cleveland, OH 44195. .... t Emory
University.
binding a positively charged species to the polyanion. This has been achieved recently' through the addition of acid. Several lines of evidence are consistent with the presence of multiple protonation states of the oxidized form of the complex, Wlo032e, HWI0O32-, and HzWIoO3," (which we will refer to subsequently as P, HP', and H2P2-,respectively), at different concentrations of acid. First, the peak or formal potentials for reduction of p4- as a function of the equivalents of added H+ per equivalent of p4- under conditions very similar to those used in the alkane photooxidation studies (cyclic voltammetry in dry CH3CN at 25 "C) show plateaus at roughly 1 and >2 [H+]/[P4-].',4 Second, the shapes of the voltammograms over this same range in [ H + ] / [ P ] indicate the presence of more than just two protonated forms of P, i.e., the existence of P,HP3-, and H2P2-.5 Third, the product distributions derived from photooxidation of representative cyclic and branched alkanes as function of [ H + ] / [ P ] are also consistent with the accessibility of p4-, HP3-, and H2P2-as [H+]/[P-] is increased from 0 to 22.1.' The collective data indicate that the P"-/P5potential is 0.65 V more negative than the HP3-/HP4potential and 1.1 V more negative than H2P2-/H2PB3potential. For H abstraction, one is interested in reducing 0 2p holes, not the empty W 5d band, so changes in the reduction potential of 0-will need to be related to the observed changes in the reduction potential of W6+. Evidence that both shift was provided by the pH dependence of the 3.80-eV (325-nm) optical absorption maximum, a transition that is 0 2p-W 5d charge transfer in character. Upon diprotonation this charge-transfer optical absorption maximum is increased by 0.09 eV from 3.80 to 3.89 eV. Thus the filled 0 2p and empty W 5d bands appear to be shifting rather uniformly and in the same direction on the energy scale when positive charge is added to the surface of the polyanion. Substantial increases in quantum yield were found for H abstraction from several alkanes when W10032k was diprotonated. The ratio of the alkane photooxidation quantum yields for H2P2to those for p4- (@H+/anoH+)depend on the particular alkane subtrate used but range from a low of -6.9 for cyclooctane, the substrate showing the least increase, to -25 for most of the alkane substrates.' While the protonated polyoxoanion was a better oxidant for this reaction, it was not kinetically competent to perform H abstraction in the absence of holes created by optical charge-transfer excitation. The lowering of the W 5d band was insufficient to activate proton transfer to 02-with electron promotion to W6+. However, upon monoprotonation, the W 5d band stabilization changes the olefin product distribution from photooxidation of 2,3-dimethylpentane and diprotonation leads to sufficient bond stabilization that the reaction R'
-
+ H2PZ-
R+ + H2P03-
(4)
dominates for cyclohexane and cyclooctane, resulting exclusively in olefin products in place of mixtures of coupled rings and olefins
0022-3654/92/2096-5658%03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vo1. 96, No. 13, 1992 5659
Alkane Reactions with Decatungstate
TABLE I: Parameters Used in tbe Calculations: hincipal Quantum Number, n ; Valence-State Ionization Potential, VSIP (eV); Slater Orbital Exponents, f (au); and Linear Coefficients, c for Doublet Orbitals (from Ref 2)
atom
n
VSIP
i-
n
P VSIP
W 0
6 2 2 1
9.50 26.98 15.09 12.1
2.641 1.946 1.658 1.2
6 2 2
7.096 12.12 9.76
S
C H
d
i-
n
VSIP
i-l
Cl
i-2
c2
2.341 1.927 1.618
5
10.50
4.982
0.6940
2.068
0.5630
0
h
WI003,"Figure 1. Structure of WlOO3:- (P-) based on the data of Sasaki et al. (Sasaki, Y.; Yamase, T.; Chashi, Y.; Sasada, Y. Bull. Chem. Sot. Jpn. 1987,60,4285).
obtained for P4- and HP3-. This was deduced from product distributions: in the presence of acid, dimer coupling to R-R ceased, the amounts of other products formed, typically olefins, increased, and the thermodynamic more-substituted olefins were formed in preference to the nonthermodynamic less-substituted olefins. This strongly suggests the radical orbital energy levels in R' lies near the W 5d LUMO in the unprotonated polyoxoyanion and above it in the protonated version. This is consistent, furthermore, with the potentials of alkyl radicals, in CH,CN, E(R'/R+), (1.2, 0.7, and 0.4 V versus N H E for primary, secondary, and tertiary alkyl radicals, respectively) as indirectly determined: versus the decatungstate potentials in the same medium (-0.6 and +0.5 V versus N H E for P4-/P*s- and HzP2-/H2P3-,respectively), measured directly by cyclic voltammetry.' It is difficult to compare the radical/carbonium ion and the decatungstate reduction potentials, however, as there are considerable experimental uncertainities in the absolute values of both sets of numbers. The difficulty with the seemingly straightforward directly measured potentials for the decatungstate species is that the Ag/Ag+ couple for the reference electrode can vary over a substantial range depending on the particular salt and supporting electrolyte used in the reference electrode chamber and other factors.' Reoxidation of the reduced decatungstate anions is catalyzed by hydrogen evolution catalysts such as Pt and R u 0 2 added to the solution. For the acidified systems, the reoxidation was very slow, compared to 200 turnovers for 4 h of irradiation for P4-. This probably reflects stronger O H bond strengths due to the stabilization of the W 5d band for H2P2-,to which an electron is promoted by OH bond formation. Alternatively, these data are consistent with the substantially lower redox potentials exhibited by the unprotonated versus the protonated forms of the complex. The binding of the alkyl radicals that are generated by H abstraction by the excited state of the decatungstate anions will also be sensitive to protonation. A theoretical discussion of C-0 bond weakening for methoxy adsorbed on a molydenum surface has appeared:* the bond strength between 02- and CH3' correlates inversely with the electron promotion energy for the reaction 02- CH3 OCH3- + e(5) Since C-0 single bonds are about l .6 eV weaker than 0-H bonds, alkoxide formation on the polyanion surfaces may be unstable. However, the extra peak in the EPR spectra of the strongly acidified one-electron-reduced, S = I / * , decatungstate (Figure
+
-
8 in ref 1) could be a transient alkylated form of the one-electron-reduced complex. Such a species could alternatively be designated an alkoxide complex of the one-electron-reduced decatungstate, and the methyl analogue, in conjunction with the general process in eq 5, would be written "OCH,2-". We have carried out an ASED-MO study of alkane dehydrogenation by P-, HP3-, and H2P2-. It is a semiempirical study which incorporates the effects of protonation by increasing the 0 and W valence orbital ionization potentials, which are input data for the ASED-MO theory, by 1 eV, with the result that all of the valence molecular orbital energies of the polyoxoanion increase in stability by about 1 eV. Thus, both the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) are stabilized by about 1 eV. It will be interesting to see whether the 0 2p to W 5d charge transfer band gap will increase 0.09 eV as observed for the diprotonated anion, H2P2-, since this is a good test of the ASED-MO theory for its ability to predict perturbation of optical spectra resulting from protonation and redox changes in solution. Rough evidence for such a capability was seen in an earlier discussion of oxygen on an iron electr~de.~ This molecular orbital band shift approach has already found success in providing qualitative predictions and interpretations of the oxidation and reduction of H 2 0on an iron electrode: anodic dissolution of an iron electrode,I0 and the potential dependencies of vibrational frequencies of C N adsorbed on an Ag electrodel' and CO on Pt electrodes.12 In the last study the CO surface structure was found to depend on potential. The esence of the calculated results and their interpretations has been that the electrode valence band shifts, induced by surface charging by the applied potentials, change the electron donor-acceptor interactions between the electrodes and adsorbed molecules and that this is responsible for the observations. In earlier work we demonstrated the importance of 0-centers to H abstraction from alkane at oxide surfaces." Such hole centers can be present as a result of nonstoichiometry, doping with cations of lower valence than the host oxide, or they can be created by optical charge-transfer excitation. A theoretical study2 has also been made of H abstraction from methane by chargetransfer-excited P4- to explain experimental observation^'^ for cyclohexene, alcohols, and other molecules. The present work improves on this last study and extends it to consider protonated
P4-. ASED-MO Method This theory15 uses atomic parameters, valence Slater orbital exponents, and valencestate ionization potentials (VSIP's) as input data and yields electronic structures and molecular binding energies. Parameters from ref 2 are in Table I. The theory is based on integrating the electrostatic forces on nuclei as atoms bind together, yielding an atom superposition energy, ER, which is repulsive, and an electron delocalization energy, ED,which, when added to ER, yields the Born-Oppenheimer energy surface E ER ED (6) E R is calculated directly from the atomic charge density distribution function, and ED is approximated as the molecular orbital electron delocalization energy from diagonalization of a modified extended Hiickel Hamiltonian
+
= -(VSIP)f
(7)
Wj = 0
(8)
W)'= 1.125(W + Z-$)Stbe4,ISR
(9)
5660 The Journal of Physical Chemistry, Vol. 96, No. 13, 1992
Jen et al.
of the p4- polyoxoanion change upon diprotonation, the change in band gap is a subtle result. It means that, given constant atomic orbital exponents, the electronic structure of a molecule depends on where the orbital energies are on the energy scale. Bands do not shift entirely rigidly up and down in response to charging.
-281
-30I
I
Figure 2. Electronic structures of P-, HP'-, and H2P2-,where P stands for W,0032.
where a and b are atom centers, S is an orbital overlap integral, and R is the internuclear distance. The molecular orbital component to this total energy is then
MMo =
Cn&ei - Eni= ia
i
(10)
where noccis the orbital occupation number (0, 1, or 2) and ei is the energy of molecular orbital i. Using this approximation to ED,we have the ASED-MO formula for the Born-Oppenheimer energy surface:
E = ER
+ AEMo
(11)
In this approximation E is generally more accurate when the pairwise atom-atom contributions to ER are calculated by integrating the force on the nucleus of the less electronegative atom that comes from the nucleus and electron charge cloud of the more electronegative atom of each pair.
Effects of Protonation on the PC Band Gap In our model we assume the structure of Pe is unchanged by protonation, We simply increase all W and 0 VSIP by 0.65 and 1 eV, representing the effects of monoprotonation and diprotonation, respectively, and recalculate the molecular orbital energy levels. Resulting bands before and after the VSIP shifts are shown in Figure 2. In modeling the shift due to diprotonation, the HOMO drops from -1 1.546 to -12.501 eV, not quite 1 eV, and the LUMO drops from -9.424 to -10.296 eV, also a bit less than 1 eV. Thus, the VSIP shift does not translate to exactly the same shift in the bands. For a qualitative study of this type there is no need to stabilize the LUMO by exactly 1 eV. The optical absorption spectra due to W 5d 0 2p excitations had a peak at 3.80 eV when the polyanion was unprotonated, and it shifted to 3.89 eV as a result of diprotonation. To reproduce absorption spectral shapes theoretically, one would have to calculate the electric dipole transition probabilities for all possible transitions and fit to a smoothing function. Instead, we will focus on the band gap. From the optical absorption band edge, the band gap is deduced to be about 3.1 eV. Our calculated band g a p are about it is 0.9 eV less. Modeling the unprotonated polyoxoanion, P-, 2.122 eV and for the diprotonated anion, H2P2-, it is 2.205 eV, so the band gap increase is 0.08 eV, essentially the same as the observed 0.09-eV peak shift when the reduction potential decreased about 1.1 V because of diprotonation. Our calculated band gap increase for the monoprotonated anion is 0.05 eV. The ASED-MO Hamiltonian appears to be doing a good job of predicting perturbations of optical spectra due to surface charging in this instance. More tests are needed to verify this as a general capability. As discussed above, the band shifting techniques of representing the effects of electrode surface charge in the ASED-MO theory have been found in more than one instance to give adsorbate vibrational and structural information in agreement with experiment. In those cases changes in donor-acceptor characteristics of the surface were responsible for the calculated results, and therefore potential-induced changes in donor-acceptor characteristics provided the interpretation for the analyzed experimental findings. While it is true that the donor-acceptor characteristics
-
Methane Activation by W1003ze* and H2Wlo0322-* In an earlier study2 some mechanistic and energy properties were calculated for the photoactivated hydrogen abstraction from methane and cyclohexene according to eq 3. Cyclohexene was known to dimerize to 3,3'-di~yclohexene,'~and ASED-MO calculations2 showed the product selectivity was a result of the weak a-H bonds allowing small activation energy barriers for H removal. This weakness stemmed from the marked stability of the allylic resonance-delocalized radical. The #?-hydrogen had a higher barrier and methane a higher one still. In the current work we use methane as a model for studying the abstraction of H from alkanes by H2P2-*. The calculations were performed using the W,012- half-cluster after it was found to have practically the same band structure as the full cluster. We note here that W60,92is a stable molecule that has a moderately strong (e = 3400 M-I cm-') absorption shoulder at 3.88 eV (316 nm).16 In the earlier theoretical study we examined H bonding to the four different types of surface oxygen on P-*. Calculated H abstraction activation energies correlated with these OH bond strengths. The calculated OH bond strengths were within 7% of one another, and terminal OH bonds were calculated to be stronger than bridging ones,though the experimental indications are that both protons and H atoms are more stable on bridging oxygen atoms." In our earlier study of methane H abstraction by Pes we determined fewer energy points around the transition-state saddle points than now. Consequently, the transition-state bond energies and structures are slightly different from those found in this study, which are based on 0.01-A OH and CH distance increments, l o H-C-H angle increments, and loo increments for orientation of the H-.CH3 axis to the anion. The activation energies calculated for bridging and terminal oxygen sites were misassigned in ref 2. The bridging oxygen abstracted H from methane with the lower, not the higher, barrier. The present calculations show a significant lowering of the activation barrier for H abstraction from CH4 over the terminal and bridging oxygen sites of the photoactivated polyoxoanion when the parameters corresponding to H2P2-are used in place of those for P-. The decrease in both barriers is about 0.28 eV, and the bridging oxygen is more active. Product (R' + hydrogenated polyoxoanion) stabilities increase 0.47 and 0.57 eV for the bridging and terminal oxygen sites as a result of the proton-induced valence band shifts in the polyoxoanion. These energy results are summarized in Figure 3, which also illustrates the calculated transition-state structures. From the structure parameters it is seen that on H2P2-* the reaction occurs sooner, with longer 0-H distances and shorter C-.H distances at the transition-state structures in accord with the Hammond postulate.'* This can be understood by recalling that the overall reaction requires the promotion of an electron from a CH u orbital to the 0 2p hole level, and this event occurs concurrently with reaching the transition state. As the oxygen band comes down in energy closer to the lower-lying CH u energy level, this process requires less energy, which is why products are more stable for H2P2-*. In H2P2-* the 0 2p hole energy level is about 1 eV more stable than but the products of H abstraction are calculated to it is in P-*, be only -0.5 eV more stable. The O H u orbital shifts down rigidly with the 0 2p band in H2P2-,becoming 1.02 eV more stable (Figure 4). Based simply on this and the change in 0 2p hole energy, the OH bond should be 1 eV stronger for H2P2-,and since it is only 0.57 eV stronger, other orbitals are destabilized by H. Orbital interactions at the transition states for H abstraction by Pe*and H2P2-* are given in Figure 5. A stabilized three-center C-Ha-0 u bonding orbital forms, and its antibonding counterpart pushes up in energy, being of the u* form between C-H and 0. The antibonding counterpart orbital experiences some stabilization
The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5661
Alkane Reactions with Decatungstate
protonated polyanion because its LUMO, which takes the promoted electron accompanying u bond formation, is more stable. This is what happens, with bond strengths between CH3' and the terminal capping 02-calculated to be 0.84 eV for P-and 1.37 eV for H2P2-. These are 2.1 eV weaker than the OH bond strengths which are calculated to be 2.93 eV for p4- and 3.43 eV for i-12P2-. These OH and OCH3 bond strengths should be decreased by -0.9 eV since the band gap is underestimated by this amount. Bond strengths to charge transfer photoexcited anions are calculated to be higher by 2.20 eV for P-* and 2.26 eV for H2P2-*. The weakness of the CH3' bonds to the two complexes suggests that they do not form, and the second EPR peak observed for one-electron-reduced complex is probably a result of a second protonation state, as suggested in ref 1. The CH3' radical orbital energy lies in the upper part of the p4- band gap, and now one must consider the possibility that alkyl radicals in general might be oxidized by it or especially by H2P2-, which has a more stable empty W 5d band. This calculation is addressed in the next section.
y1 28 81
-1
,
I
I,
0 I
0.2+,
/
o.i/
OZ,,'
'I!\
CH4+(H2P2.)'
'\
'\-0.04 \-
CH4+(H2P2.)* '>,-0.35 CH3 * + H3P" CH3 * t H3P2'j,
-
u.1
Figure 3. Energetics and transition-state structures for H abstraction from methane over P"- and H2P2-.
:I
-10
u u j w 5d
,
-_-_-_
Figure 4. Formation of u bonds between H and terminal 0 in p-and H2P2-.
Figure 5. Transition-state electronic structures for H abstraction from terminal 0 in P"- and H2P2-.
CH, by
through mixing of the high-lying CH u* orbital in a way that decreases the orbital amplitude on H and reduces the antibonding destabilization of the C-Ha-0 u* orbital. It is clear from Figure 5 that the C-He-0 u* orbital is the vehicle which promotes an electron to the 0 2p hole. When the hole level is stabilized, this antibonding orbital loses an electron sooner, so the transition states should come sooner, and with a lower barrier. This is what happens in the calculations.
Binding of Alkyl Radicals to P"- and HzP2The methyl radical is our prototype for alkyl radical binding to 02-on these anions. CH3' should bind more strongly to the
Formation of Alkyl Cations We have optimized the structures of CH3', the primary carbon radicals CH3CH;, the secondary carbon radicals (CH3),CH' and chair form cyclohexyl C6HI and the tertiary carbon radical (CH3)3C'. The radical energy levels vary respectively as follows: methyl, -9.76 eV; primary, -9.60 eV; secondary, -9.42 and -9.33 eV; tertiary, -9.25 eV. These may be related in a qualitative way to observed' product distributions as follows: In P-the bottom of the W 5d band is at -9.42 eV, so the lack of dimerization of 2,3-dimethylpentane is understandable, for tertiary radicals will dominate upon H abstraction and these will be oxidized by P-. Cyclohexane and cyclooctane will form secondary radicals, and their radical electron energies are about the same as the PLUMO energies, so a mixture of dimer and olefin products is obtained. Monoprotonation lowers the LUMO to -9.99 eV and does not affect this distribution but diprotonation, which lowers it to -10.30 eV, gives entirely alkene products. The lack of agreement of the simple energy level picture in predicting product distributions precisely, for based on it HPf should lead exclusively to olefins for the secondary radicals, is due to errors in the calculated energy levels and structural and kinetic details of electron transfer. However, the trend toward decreasing CH bond strengths and decreasing radical electron stabilities for the series tertiary < secondary < primary agrees with the observations of ref 1. Concluding Comments This has essentially been a study of the interaction of radicals (H' and CH3') with a closed-shell anion (02-) and an open-shell anion (0-). Radical bonds are always strong with the open-shell anion, and they are weak with the closed-shell one because the R-O*- bond order is due to two electrons in the u orbital and one in the u* orbital. When acceptor orbitals are around, such as the 5d orbitals on W6+, they remove the electron from the u* orbital, thereby stabilizing the R-O bond. More stable acceptor orbitals stabilize the R-O bond more, and when the R' radical orbital is relatively unstable, as for alkyl radicals compared to H atoms, oxidation to R+ must be considered. We have given form to these concepts through ASED-MO calculations on and the stronger oxidant H2P2-,explaining their ability to abstract H from alkyl molecules when photoactivated, creating 0-, and their ability to oxidize the resulting alkyl radicals. Acknowledgment. A.B.A. thanks the B.F. Goodrich Co. for awarding a graduate fellowship which supported S.-F.J., a n d C.L.H. thanks the National Science Foundation (Grant CHE90223 17) for support.
References and Notes (1) Renneke, R.F.; Kadkhodayan, M. P.; Pasquali, M.; Hill, C. L. J . Am. Chem. Soc., in press. (2) Awad. M.K.; Anderson, A. B. J . Am. Chem. SOC.1990, 112, 1603. (3) Keita, B.; Nadjo, L. Muter. Chem. Phys. 1989, 22, 77. (4) Figure 3s in the supplementary material for ref 1. ( 5 ) Pasquali, M.;Hill, C. L. Unpublished work.
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J . Phys. Chem. 1992, 96, 5662-5667
(6) Eberson, L. Electron Transfer Reactions in Organic Chemistry; Springer-Verlag: Berlin, 1987, p 46 and references therein. (7) (a) CRC Handbook of Chemistry and Physics, 71st ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1990; pp 8-16. (b) Mann, C. K.; Barnes, K. K. Electrochemical Reactions in Nonaqueous Systems; Marcel Dekker: New York, 1970; p 26. (8) Shiller, P.; Anderson, A. B. J . Phys. Chem. 1991, 95, 1396. (9) Anderson, A. B.; Ray, N. K. J . Phys. Chem. 1982, 86, 488. (10) Anderson, A. B.; Debnath, N . C. J . Am. Chem. SOC.1983,105, 18. (11) Anderson, A. B.;KBtz, R.; Yeager, E. Chem. Phys. Lett. 1981,82, 130. (12) Mehandru, S.P.; Anderson, A. B. J . Phys. Chem. 1989, 93, 2044. (13) Moo3: Mehandru, S.P.; Anderson, A. B.; Brazdil, J. F.; Grasselli, R. K. J . Phys. Chem. 1987, 91, 2930. Bi203: Mehandru, S. P.; Anderson,
A. B.; Brazdil, J. F. J. Chem. Soc., Faraday Trans. 1 1987,83,463. CuMoO,: Ward, M. D.; Brazdil, J. F.; Mehandru, S. P.; Anderson, A. B. J. Phys. Chem. 1987, 91, 6515. MgO: Mehandru, S. P.; Anderson, A. B.; Brazdil, J. F. J . Am. Chem. SOC.1988, 110, 1715. (14) Yamase, T.; Usami, T. J . Chem. Soc., Dalton Trans. 1988, 183. (15) Anderson, A. R. J . Chem. Phys. 1975,62, 1187. Anderbw, A. B.; Grimes, R. W.; Hong, S. Y. J. Phys. Chem. 1987, 91, 4245. (16) Nomiya, K.; Sugie, Y.; Aminoto, K.; Miwa, M. Polyhedron 1987,6, 519. (17) Day, V. W.; Klemperer, W. G.; Maltbic, D. J. J. Am. Chem. SOC. 1987,109, 2991. Day, V. W.; Klemperer, W. G.; Schwartz, C. J. Am. Chem. SOC.1987, 109, 6030. (18) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic Chemistry, 3rd ed.; Harper & Row: New York, 1987; pp 212-4.
Dielectric Relaxations of Small Carbohydrate Molecules in the Liquid and Glassy States Timothy R. Noel, Stephen G. Ring, and Mary A. Whittam* AFRC Institute of Food Research, Colney Lane, Norwich, Norfolk NR4 7UA, UK (Received: October 28, 1991; In Final Form: February 24, 1992)
Dielectric permittivity and loss of a number of liquid and vitreous monosaccharides have been measured over a range of frequencies from 100 to lo5 Hz and temperature range -100 to 150 O C . In all cases either one or two relaxations were observed depending on the carbohydrate molecule; these occurred either just above the calorimetric Te in the case of a single relaxation or both above and below Tgwhere two relaxations were observed. Fitting the relaxations to the Arrhenius equation, the sub-T, (or secondary) relaxation had an activation energy of approximately 45 kJ/mol in the two cases where it was observed. The primary relaxation activation energy varied from 177 to 353 kJ/mol depending on the monosaccharide. An explanation for the different values of activation energy is given in terms of the molecular structures of the monosaccharides, primary alcohol moieties conferring higher activation energies than those of similar molecules without primary alcohol groups. The lowest activation energies were observed for the noncyclic alditols xylitol and glucitol.
Introduction Dielectric spectroscopy has been used increasingly to study biological systems and, in particular, the behavior of their constituent water molecules.’ However, even simple solutions give rise to quite complicated spectra which are then difficult to interpret unambiguously. With recent interest in vitrification and its implications in cryobiology* a number of studies have been reported on carbohydrates and their aqueous solutions. These have included investigations not only by dielectric spectroscopy3-* but also by techniques such as depolarization thermocurrent meas u r e m e n t ~and ~ electron spin resonance.’O A major effort has been directed at understanding the interactions of water with other molecules, due to the importance of water in maintaining biological structure and function, the consequences of removal of mobile water by freezing or drying being severely deleterious in many cases. In order to identify the interactions between the different components, for example, carbohydrate molecules and water, it is important to understand first the behavior of the individual components. The dielectric relaxation behavior of water molecules has been examined in some detail,” but relatively few studies have been reported on pure, dry carbohydrates. Vitrification is marked by a discontinuous change in properties which are second derivatives of the free energy, such as heat capacity and thermal expansion coefficient. This has lead to the proposal that there is a second-order thermodynamic phase transition underlying the vitrification process. Kinetic factors, however, determine the temperature of the transition, Te;thus, the value of Te depends on the time scale of the observation or conversely on the frequency characteristics of the experimental probe. The glass transition is also accompanied by a change in the rate of molecular translational and rotational diffusion.l* By dielectric spectroscopy, peaks which correspond to characteristic relaxation processes within the sample can be observed. The primary or a-relaxation, which is observed a t the highest temperature (or lowest frequency), has generally been associated with the increase in molecular mobility which occurs on heating through
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the glass transition. Secondary or fl-relaxations are also observed in many materials at lower temperatures (or higher frequencies) than a-relaxations; however, their origin is still the subject of some debate.I3 From measurement of the frequency and temperature dependence of dielectric relaxations, it is possible to obtain estimates of the activation energies of the physical processes from which the relaxations arise. These energies may in turn provide information on the processes themselves or even, perhaps, on the molecular structure or arrangement. In general, it is found that energies associated with a-relaxations are greater than those of 8-relaxations, sometimes by an order of magnitude. Various interpretations have been put forward for the Occurrence of these relaxation processes. Johari has proposed a modelI3 whereby structural nonuniformity within a glass leads to “islands of mobility” which are responsible for the secondary relaxation, while the primary relaxation is due to larger, cooperatively rearranging regions. According to this model, specific details of molecular structure are not required for the interpretation. A slightly different approach14which depends more on the specific molecular structure proposes that a- and 8-relaxations depend on the average free volume and the free volume fluctuations, respectively. In this latter model, fluctuations in free volume provide the space necessary for motion of bulky side groups to occur. In this paper, we investigate both a- and @-relaxation behaviors of six dry carbohydrate molecules and note how their relative activation energies vary as a function of their molecular structures.
Materials and Methods D-(+)-Glucose (mixed anomers), &(+)-galactose, &(+)-xylose, and D-(-)- and L-(+)-arabinose, glucitol, and xylitol were purchased from Sigma Chemical Co. and were used without further purification. Chemical structures are presented in Figure 1. Approximately 10 g of the crystalline form was dried under vacuum over PzOs for at least 24 h at 60 OC, after which the material was considered dry. The crystals were then heated to 1992
American Chemical Society
