5662
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
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
0022-3654/92/2096-5662$03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 13, I992 5663
Dielectric Relaxations of Small Carbohydrates H
H
bH
D-Xylose
CHlOH I HCOH I HOCH I HCOH I HCOH I CHzOH
H
33 mm) was used for measurements of capacitance and dissipation factor over the frequency range 20-105 Hz. Temperature was controlled between -100 and 150 OC using a liquid N2 cryostat (Planer Products,Sunbury on Thames, England) for temperatures below ambient while heating was achieved using earth screened resistive elements in a demountable oven. Temperature was measured using a 100-ohm platinum resistance element with typical temperature differences between sample and sensor quoted as I1 "C (Polymer Laboratories, Loughborough). The apparatus was purged with N2to minimize water sorption into the sample during measurements. Sample thickness was between 0.5 and 1.O mm, and in each experiment the values of cell constant and adjustment due to stray capacitance were incorporated using the software provided (Polymer Laboratories). Performance of the instrument was routinely checked against measurements taken with a known air gap between the plates of the cell. For experimental samples, two types of measurements were carried out; series of isothermal measurements were taken at a number of frequencies across the available range, and isochronal measurements were taken as temperature was scanned upward at a rate of 1 OC min-' using a programmable temperature controller (Polymer Laboratories).
t)H
GArabinore
CHzOH I HCOH I HOCH I HCOH I CHzOH
Glucitol
Xylitol
Figure 1. Chemical structures of the carbohydrates used in this study.
just above melting point in a sealed tube. Alternatively, samples were melted and then dried in the glassy form and reheated just before use. If necessary, samples were degassed while hot to remove any opacity; all samples were obtained and used as clear liquids. Care was taken to avoid caramelization, which was apparent as a yellow discoloration in preparations which were left for extended times at high temperatures. Melts were quenched rapidly to -100 OC in the dielectric analyzer to avoid recrystallization. A dielectric thermal analyzer (Polymer Laboratories, Loughborough) equipped with a General Radio Model 1689M Precision RLC Digibridge and stainless steel parallel plate cell (diameter 20
Results Representative curves showing temperature scans at constant frequency (isochrones) of the dry carbohydrates are shown in Figure 2. In the case of glucose and galactose, peaks were observed at two temperatures, one just above the glass transition temperature of the sample (see Table I for values of T ) and another one some tens of degrees lower. The height of the kigher temperature peak (corresponding to the primary relaxation) was an order of magnitude greater than that of the lower temperature (secondary relaxation) peak. The two relaxations are therefore plotted separately in the figure for better resolution of the smaller peaks. Using the 1-kHz isochrone for comparison, peaks were observed at -56.5 and 61 "Cfor galactose and at -68.5 and 60.5 O C for glucose. With increasing frequency the separation between the two relaxation temperatures decreased, since the position of the secondary relaxation shifted to a greater extent with temperature than did that of the primary relaxation. The height of the secondary relaxation peak also diminished with decreasing
'24r
01
-90 Temperature ("C)
2b
'
-80
I
-70
1
1
t
-60 -50 -40 -30 Tomporatun ("C)
1
-20
'
-IO
L
0
Figure 2. Plots of dielectric loss against temperature for (a) primary relaxation of xylose and (b) secondary relaxation of galactose a t a range of frequencies.
5664 The Journal of Physical Chemistry, Vol. 96, No. 13, I992 TABLE I: Glass Transition Temperatures and Temperatures of Primary Dielectric Relaxations (at 1 kHz) for the Carbohydrates Used in This Study As Determined by Differential Scanning Calorimetrv'5 D-(+)-glUCOSe D-(+)-galactose D-( +)-xylose L-(+)-arabinose D-(-)-arabinose glucitol xylitol
38 32 13 4 2 0 -19
60.5 67 31.5 33 26.5 10.5 -14
Noel et al. I
1.2,
0.0
'
-
2
-
1
0
1
2
3
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4
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:I
:*$E 0.6
1
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0.0 -2
-1
,
,
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Figure 4. Normalized plots of dielectric loss against frequency for (a) xylose and (b) glucitol.
Br
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32-
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31 20 F Y -
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"
30
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Figure 3. Dielectric loss plotted as a function of frequency for (a) xylose and (b) galactose.
temperature whereas the opposite was in general found for the primary relaxation peaks. All of the carbohydrates studied displayed a primary relaxation a t a temperature just above Tg(as determined by differential scanning calorimetry, see Table I); however, no secondary relaxation could be observed in the available temperature range for the carbohydrates xylose, arabinose, glucitol, and xylitol. Assuming a similar separation for the primary and secondary relaxations of these latter molecules, some indication I 0 08 of a low-temperature peak, if present, should have been seen at -80 -60 -40 -20 0 the lowest temperatures achieved, but this was never observed. Temperature ('Ci Due to experimental limitations in frequency and temperature, Figure 5. Maximum loss, c'',,,~.,plotted against temperature for (a) isothermal measurements of dielectric loss, e'', enabled only primary relaxation peaks of xylose ( 0 ) ,glucose ( O ) , galactose (m), and primary relaxation peaks to be detected. as shown in Figure 3 for arabinose (A) and for (b) secondary relaxation peaks of galactose (m) and glucose ( 0 ) . galactose and xylose. Half-widths of the peaks (i.e., width at half-maximum peak height) spanned several decades. The proand galactose, plotted this time from the isochronal data, is also gressive decrease in peak height with increasing temperature characteristic of a primary relaxation can again be seen. A presented. It is apparent that while the primary relaxation peak diminishes with increasing temperature, apart from the case of representative normalized plot of reduced frequency (j'/fmax) against ~ " / d is' presented ~ ~ in Figure 4 for xylose, together with arabinose where little temperature effect is discernible, the reverse is true for the secondary relaxation. the reduced plot for glucitol showing the unusually asymmetrical The complex plane plot of dielectric permittivity, e', and loss, shape of the relaxation spectrum for this particular molecule. d', is presented in Figure 6 for xylose. Similar plots were obtained Figure 5 shows how e''mx varied with temperature for the primary relaxation of glucose, galactose, xylose, and arabinose. A plot for the other carbohydrates. With the available frequency range, of e"- versus temperature for the m n d a r y relaxations of glucose a major portion of each curve could be obtained at any one tem-
'
The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5665
Dielectric Relaxations of Small Carbohydrates
6
8
10
12
14
16
18
20
22
24
26
28
30
E‘
Figure 6. Complex plane plot for xylose at 30.5, 35.5, 40.5, 45.5, and 50.5 OC. Frequencies in kilohertz are given next to the data points.
perature. Higher temperatures enabled the lower frequency part to be plotted, while low temperatures shifted the plots to the high-frequency end. At high frequency the curves at different temperatures merged, whereas the low-frequency limit of permittivity, eo, decreased with increasing temperature in all cases. While this shift in eo was relatively small for glucose, galactose, xylose, and arabinose, it was more pronounced for the acyclic molecules xylitol and glucitol. For these two carbohydrates a 5deg temperature change caused a change in eo of around 1.5 over the range of temperatures used in this study. The actual values of c,, for glucose, galactose, arabinose, and xylose were similar at the same temperature; however, comparison with xylitol and glucitol was difficult because complex plane plots of the latter were only obtained at much lower temperatures. Extrapolation would suggest that these carbohydrates, too, might have c,, values similar to the others. The value of the Cole-Davidson equation16was found to be 0.30 for glucose, which is close to the value of 0.34 reported by Johari and co-~orkers,~ while that of glucitol was found to be 0.13 in agreement with a previously published value* (0.14).
I
Representative plots of frequency of the loss peaks against reciprocal temperature are given in Figure 7. In all cases the data were fitted to the Arrhenius equation where E represents the activation energy of the relaxation process. Values of these energies for both primary and secondary relaxations are given in Table 11, together with the 9 values of the linear regression.
Discussion a-and @-Relaxations.An interesting result of this study is the observation of both a primary (a)and a secondary (8) relaxation peak for certain carbohydrate molecules (glucose and galactose) but only a single primary relaxation peak for the other carbohydrates studied. While the primary relaxation process can be attributed to the changes in mobility associated with the glass transition, the origin of the secondary relaxation process remains more speculative. Models for the relaxation mechanisms are either ergodic or nonergodic, the former implying that all molecules are capable of contributing to the secondary relaxation and the latter suggesting that only a fraction of the total number of molecules can do so. Both models explain certain aspects of observed relaxation behavior while failing to account adequately for others. In one nonergodic model,I3 rigid cagelike structures within a glass are considered to enclose regions of low density wherein molecular orientation and translational motion persist and give rise to secondary relaxation, while primary relaxation is considered to be the result of larger scale, cooperative motion. Thus, the two relaxations are the result of nonuniformity of glass structure. Under these conditions all amorphous solids, regardless of specific molecular composition of structure, should exhibit both a-and &relaxations. It is possible that in our studies &relaxations, although present, are not observed simply because they occur beyond the experimental range of temperature and frequency
I 2.4
2.8
3.2
3.6
‘/T
4.0
4.4
4.8
5.2
5.6
103 (K-’)
Figure 7. Arrhenius plots for primary ( 0 )and secondary (e)relaxations of glucose.
available. This in itself would be an interesting observation, particularly for xylose and arabinose which show similar a-relaxation behavior to glucose and galactose (albeit at a temperature lower by about 30 “C)yet fail to show any ,!?-relaxationat the temperatures one might expect by extrapolation of the behavior of glucose and galactose. Another explanation for the nonappearance of &relaxation is that certain materials may manifest such relaxations mechanically while being dielectrically inactive; however, once again the similarity of the molecules used in this study would lead one to expect similar general behavior. The presence of secondary relaxation peaks for some aliphatic alcohols but not for others has been observed previously17 and the nonappearance of 8-relaxation peaks attributed to their possible Occurrence outside the experimentally available range. An alternative ergodic modelL4invokes density fluctuations to account for the observation of j9-relaxations. Local variations of free volume within an amorphous polymer matrix provide “holes” of a sufficient size for motion of certain molecular groups (in this case that of phenyl groups attached to polycarbonate), giving rise to the &relaxation. These “holes” are too small to permit motion of the much larger units which participate in the a-relaxation. In this way all molecules are statistically capable of contributing to both the a-and the 8-relaxation processes. It is tempting to extend this idea to our lower molecular weight system and to
5666 The Journal of Physical Chemistry, Vol. 96, No. 13, I99‘2
propose that the observed @-relaxations for glucose and galactose are due to motion of the primary alcohol part of the molecules. Xylose and arabinose, while being very similar to glucose and galactose in other respects; lack this hypothetically more mobile CH20H group and therefore, according to this model, do not show any secondary relaxation process. It is difficult to compare the behavior of the linear molecules glucitol and xylitol since their relaxations take place at lower temperatures than those of the cyclic molecules, so any &relaxation would probably occur below our experimental temperature range. Once again, there are objections to the model-for example, on the grounds that it does not adequately explain experimentally observed annealing behaviorI3-and certainly it would be satisfying to have a model which did not rely on details of molecular structure to explain such a widely observed phenomenon. A final possible explanation for the nonappearance of secondary relaxation peaks for certain carbohydrates might be that their magnitude was too small for detection at the resolution level of the apparatus. Conversely, it might be argued that those secondary peaks which were observed were due to impurities within the samples; however, similar results have been reported by other authors for the dielectric relaxation of glucose7 supporting the present observations. Loss Relaxation Spectra. The relaxation spectra shown in Figures 3 and 4 give an indication of the width of distribution of the a-relaxation times for the various carbohydrate molecules. For a Debye-type single relaxation time, a half-width of 1.14 decades is expected; the a-relaxations observed in this study involved a wider distribution of relaxation times as demonstrated for xylose in Figure 4. The half-widths did not appear to be influenced much by temperature. For glucose, the half-width was 2.3 decades, in agreement with the value observed previously by Johari and co-workers7 (also quoted as 2.3), and the galactose relaxation spectrum had a half-width of 3.3 decades, whereas the values for xylose and arabinose were 1.9 and 2.0, respectively. This difference in half-width is clearly demonstrated in Figure 3, which compares the rather wide relaxation peaks of galactose with the much narrower ones of xylose. The reason for the much broader relaxation spectra of galactose compared to the other molecules is unclear. One possible explanation might be the presence of water in the sample (which has been demonstrated to cause broadening of the a-relaxation of glucose7). However, this is unlikely in view of the high temperature of the observed a-relaxation peak; the presence of water in the sample would have caused a reduction in Tgand hence a reduction in the temperature at which the a-relaxation was observed when compared to the value quoted in Table I for the dry carbohydrate. The shape of the glucitol relaxation spectrum was different from those of the other carbohydrates studied, also demonstrated in Figure 4, in that it was highly asymmetrical making determination of a half-width difficult. This type of behavior has been reported previously for glucitol,8 and it has been suggested that the distortion on the high-frequency side of the spectrum is due to the presence of a secondary relaxatione6 If this were the case, then we would also expect to see similar distortion of the relaxation spectra of glucose and galactose, both of which exhibit &relaxations; however, Figures 3 and 4 demonstrate that this is not observed. Temperature Depenaence of the Lass RelaxatiOn From the plots of maximum dielectric loss against temperature (Figure 5 ) it appears that the strength of the main, a-relaxation decreases with increasing temperature for glucose, galactose, and xylose whereas the strength of the L-arabinose a-relaxation appears unaffected by temperature over the experimental range. Conversely, the strength of the @-relaxationfor the two cases where it was observed increases with temperature. In terms of the nonergodic model this might be ascribed to increasing numbers of molecules joining the “islands of mobility” at the expense of the molecules involved in the rigid cagelike structure. In terms of the density fluctuation model, it can be argued that the density of a glass will decrease with increasing temperature. This will lead to greater fluctuations in local free volume, enabling more frequent 8-relaxations.
Noel et al. TABLE II: Activation Energies AE for the Primary (a)and Secondary ( B ) Dielectric Relaxation Processes of Dry Carbohydrate Molecules (Values of r* for Fit to Arrhenius Equation in Parentheses) carbohydrate molecule AE, (kJ/mol) AER(kJ/mol)
D-(+)-glucose D-(+)-galactose D-( +)-xylose D-(+)-arabinose L-(-)-arabinose glucitol xylitol
305 (0.998) 366 (0.973) 235 (0.999) 219 (0.997) 238 (0.993) 194 (0.994) 207 (0.987)
42 (0.994) 49 (0.999)
not observed
not observed not observed not observed not observed
Conversely, the orientational correlation of the molecular dipole moments decreases with temperature, causing the observed decrease in strength of the a-relaxation. The complex plane plot presented in Figure 6 is of the form of an arc skewed at the high-frequency end and which shifts with temperature at the low-frequency end. ColeDavidson fi parameters measured from these plots varied from 0.33 for xylose to 0.1 3 for glucitol, smaller values indicating a wider distribution of relaxation times in agreement with the observed loss relaxation spectra (Figures 3 and 4). Activation Energies. For all the observed relaxation processes activation energies were computed from straight-line fits to the data, which assumes Arrhenius-type behavior. In the cases where the data fitted less well to a straight line (lower values of 9 in Table 11), gradients increased with decreasing temperature in a similar fashion to that predicted by the Vogel-Tamman-Fulcher equation, f, = A exp(-B/(T - To)). Attempts to fit the data to this equation, however, were generally unsuccessful. From the Arrhenius plots of glucose and galactose for which two relaxations were observed (Figure 7), it appears that the a-and @-processes would merge at high temperature. This might be difficult to observe in practice, however, due to the decrease in strength of the a-process with increasing temperature. Calculated values of the 8-relaxation activation energy are similar for glucose and galactose (42 and 49 kJ/mol, respectively). These values are somewhat lower than those reported previously for glucose/water mixtures7 (-60 kJ/mol) but are certainly of the order of magnitude generally expected for &relaxations18 and are considerably lower than those for the main relaxation (Table 11). Activation energies for secondary relaxations have previously been demonstrated to depend on molecular size,lg so the similar values found for glucose and galactose in this study may simply reflect the similarity in molecular size of the two carbohydrates. Further studies using carbohydrate molecules of different sizes and with different types of side group might yield more information on the origin of the 8-relaxation and its dependence (or otherwise) on molecular structure. a-Relaxation energies, on the other hand, did appear to depend on molecular size. The carbohydrates studied could be roughly classified into three groups according to their activation energies; glucitol and xylitol had the lowest values of AE, and galactose and glucose had the highest values of activation energy, while arabinose and xylose showed intermediate behavior (Table 11). Activation energies therefore increased in the order linear molecule > cyclic pyranose molecule > cyclic pyranose molecule with primary alcohol group, Le., roughly in order of molecular volume. Differences in activation energies between the linear and furanose molecular were however less pronounced than those of the molecules containing the primary alcohol group. It has been suggestedEthat activation energies of supercooled glucitol and other polyols depend to some extent on hydrogen bonding, which is in turn dependent on molecular size and structure. Differences in hydrogen bonding may therefore account, at least in part, for the different activation energies observed in this study. Comparison of D- and L-arabinose relaxations indicates that while their activation energies are similar (Le. the slopes of the Arrhenius plots), the two curves are nevertheless shifted with respect to temperature. Thus, the D-arabinose relaxation takes place at lower temperature than the L-arabinose relaxation over the range of experimental frequencies used. This would imply that the two optical isomers
J. Phys. Chem. 1992, 96, 5667-5668 have different glass transition temperatures, an observation which is confirmed calorimetrically (Table I). Registry No. D-(+)-Gluwse, 50-99-7; D-(+)-galactose, 59-23-4; D(+)-xylose, 58-86-6; D-(-)-arabinose, 10323-20-3; L-(+)-arabinose, 5328-37-0; glucitol, 50-70-4; xylitol, 87-99-0.
References and Notes (1) Kaatze, U. Phys. Med. Biol. 1990, 35, 1663. (2) Aneell. C. A. Annu. Rev. Phvs. Chem. 1983. 34. 593. (3j Abadie, P.; Charbonni5re, R.,Gidel, A.; Girard, P.; Guilbot, A. C. R . SLances Acad. Sci. 1956,242, 1016. (4) Tait, M. J.; Sugget, A.; Franks, F.; Ablett, S.;Quickenden, Y. A. J . Solution Chem. 1972,-i,131. (5) Pottel, R.; Adolph, D.; Kaatze, U. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 278. (6) Angell, C. A,; Smith, D. L. J . Phys. Chem. 1982,86, 3845. (7) Chan, R. K.; Pathmanathan, K.; Johari, G. P. J . Phys. Chem. 1986, 90, 6358.
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(8) Naoki, M.; Katahira, S. J . Phys. Chem. 1991,95, 431. (9) Pissis, P.; Diamanti, D.; Boudouris, G. J . Phys. D Appl. Phys. 1983, 16, 1331. (IO) Roozen, M. J. G. W.; Hemmings, M. A. J . Phys. Chem. 1990, 94, 1326. (1 1) Franks, F. Water, a Comprehensiue Treatise, Plenum: New York, 1982; Vol. 7. ( 1 2) Franks, F. Biophysics and Biochemistry at Low Temperatures; University Press: Cambridge, 1985; Chapter 3. (13) Johari, G. P. J . Chim. Phys. (Paris) 1985,82,283. (14) Ngai, K. L.; Rendell, R. W.; Yee, A. F. Macromolecules 1988,21, 3396. (15) Orford, P. D.; Parker, R.; Ring, S.G. Carbohydr. Res. 1990,196,1 1 . (16) Davidson, D. W.; Cole, R. H. J. J . Chem. Phys. 1951, 19, 1484. (17) Johari, G. P.; Goldstein, M. J . Chem. Phys. 1971,55, 4245. (18) Johari, G. P. In Relaxations in Complex Systems; Ngai, K. L., Wright, G. B., Eds.; Naval Research Laboratory: Washington, DC, 1985; p 17ff. (19) Ahmed, M. S.;Crossley, J.; Hossain, M. S.;Kashem, M. A.; Saleh, M. A.; Walker, S. J . Chem. Phys. 1984,81, 448.
COMMENTS Comment on “Monltorlng Partlcle Slze Changes of a Supported Phase by ESCA”
Sir: In a recent paper,’ Hoffmann, Proctor, Houalla, and Hercules (HPHH) reported on electron spectroscopy for chemical analysis (ESCA) spectra of Fe/A1203 catalysts. Although the paper certainly advances our understanding of the surface composition and structure of supported heterogeneous catalysts, some of the authors’ conclusions appear unwarranted. A central issue in HPHHs paper is monitoring of the Fe-to-Al photoemission intensity ratios as a function of both the particle size and Fe loading. The authors relate the Fe 2p3/2 area-rather than the entire Fe 2p3/2;./2 area-to the growth mode of the active phase up to one monolayer. The rationale is that the Fe 2p/A1 2p intensity ratios measured for low-Fe catalysts systematically overestimate the Fe content relative to the theoretical intensity ratio curve, as derived from the Kerkhof-Moulijn (K-M) model2 (the “monolayer line” in Figure 3 of ref 1). They conjecture that the main source of error derives from the integral background approximation used.3 They also find that this error becomes even greater if a Tougaard background4 is used. I feel that the above experimental results alone are not sufficient to justify the conclusions that the use of the Fe 2p area overestimates the iron content and that the Tougaard background is not accurate enough for these catalyst systems. Such an overestimation of iron is only apparent and may be explained with the following arguments: (i) The first argument concerns some of the parameters (listed in Table I1 of ref 1) that were used to derive the K-M line of Figure 3B,C. A major error can be associated with the intensity-energy response of the photoelectron spectrometer. HPHH assume that the overall response transmission/detector efficiency, D,of their AEI ES 200 instrument-operated in the fixed retardation ratio mode-is proportional to photoelectron kinetic energy. This (theoretical) assumption may be in striking variance with the actual intensity-nergy response of a specific instrument, particularly for such wide energy separations as that existing between the A1 2p peak and the Fe 2p band (around 630 eV).S-7 A minor error may be associated with the electron inelastic mean free paths, A. In Table I1 of their paper HPHH use the Penn formalisms for calculating X values. In fact, it is the electron attenuation length, AL, that is relevant to ESCA.799J0 Although exchange in terminology (and symbols) has often occurred in the literature, X and AL each have a separate physical meaning9
Apart from semantics, and following the assumption of HPHH, ALA’2p = 18 A, use of Penn’s formula gives ALF, 2p = 1 1.2 A, versus the value of 13.3 A derived from the Seah and Dench formalism,1° which provides a more accurate estimate of A L k 7 It should parenthetically be noted that uncertainties in both D and AL(X) affect the accuracy of the calculated mean particle sizes of the active phase which are derived via eqs 2-4.’ (ii) A second argument pertains to the different ways the authors use for measuring the iron photosignal areas, whether referring to the whole Fe 2p or to Fe 2p3 alone (Figure 5 of ref 1). In the first case, they include the high binding energy “shake-up” structure for both the 312 and 112 spin-orbit terms, whereas in the second one they exclude the intensity of the satellite. The latter procedure is wrong. HPHH relate the measured intensities to Scofield’s photoionization cross sections,” which were calculated within the one-electron, frozen-orbital model (Koopmans’ theorem). In this context, sudden approximation arguments12 show that all the intensities of a particular photoemission transition must be considered for quantitative purposes, Le., that of the “adiabatic” peak plus that of the satellites originating from electron configuration interaction effects. As a consequence, the Fe 2p/A1 2p intensity ratios reported in Figure 3 are a more faithful witness to the quantitative composition of the materials than the Fe 2p3/,/A1 2p intensity ratios, and their apparent overestimation of the iron content for low-Fe catalysts is probably due to errors associated with the K-M monolayer line, as discussed in paragraph i. Also,the apparent better agreement given by the Fe 2p3/,/Al 2p ratios could result merely from fortuitous canceling out of errors contained in the calculation of the K-M line and in the measurement of the Fe 2~312intensity. Some years ago, I reported on quantitative ESCA results of iron oxides as well as of Fe203+ A1203 mixture^'^-'^ using a “first principles model”’ which included Scofield’s cross sections. I found that both the nO/nFe and nFe/nAl atomic ratios were accurate to &lo% relative error when the “shake-up” structure was considered as a part of the Fe 2~312intensity, whereas severe underestimations of the iron content were obtained when only the intensity of the leading peak was accounted for.I3 These findings were useful for studying the surface composition of Fe/A120316*17 and Fes2B,8/A1203’ssmall particle systems. To conclude, while it is not my intention to establish what is the background to use for measuring the Fe 2p area, nor to settle the question of whether use of the integral background o r use of a Tougaard background introduces less error into the ESCA Fe
0022-3654/92/2096-5661$03.00/0 0 1992 American Chemical Society
