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J. Phys. Chem. wa2, 86,5128-5133
Application of the Method of Time-Lag Analysis to the Study of Diffusion in Solids of Nonhomogeneous Macroscopic Structure C. Savvakls and J. H. Petropoulos’ Physical Chemistry Laboratory, Demokritos Nuclear Research Center, Aghb Paraskevi, Athens, Greece (Received: February 8, 1982)
The study of the anomalous diffusion of N2 in microporous graphite compacts is carried further here by systematically varying the mode of compaction. It is then shown that the results of the method of time-lag analysis, introduced and applied for the first time in previous papers, can be successfully correlated with the axial nonhomogeneity of the macroscopic structure of the compacts through a suitable physical model presented earlier. Previous conclusions about the nature of “non-Fickian” diffusion of gases in microporous compacts are confirmed and extended. The results of time-lag analysis also point to an unusual structural feature of the graphite porous solids studied here as compared with analogous ceramic or metallic compacts. This feature is confirmed by means of independent more direct techniques and explained in terms of the properties of graphite. The present results are also important from a more general viewpoint: they demonstrate the ability of the method of time-lag analysis to furnish information about the overall axial nonhomogeneity of diffusion media which are structurally inhomogeneous also in the radial direction.
Introduction In previous paperslW3a general method of time-lag analysis was developed and shown to be of great potential value for the investigation of diffusion phenomena which deviate from normal (“Fickian”) diffusion kinetics. The method was then used in our laboratory for the investigation of the diffusion of simple gases in porous solids made by uniaxial powder c o m p a c t i ~ n . ~ ? ~ Compaction of powdered solids is usually carried out by compression in a cylindrical die and generally produces pellets of nonuniform density of packing (or porosity).6 This means that the sorption and diffusion properties of the compacted solid can, in turn, be expected to be nonuniform. Variation of the diffusion (DT) and sorption or solubility ( S )coefficients along the direction of diffusion X (which is here the same as the direction of compression) is of particular importance, because it can lead to very marked deviations from Fickian diffusion kinetic^.^!^ The X dependence of DT,S in powder compacts was first put in evidence directlp by showing that the effective diffusion coefficient changed when the thickness of the pellet, 1, was successively reduced (by grinding the pellet down) and indirectly7 by reinterpretation of anomalous time-lag data reported by Barrer et al.9 There remained a difference of opinion, however, regarding the time-lag anomalies observed in “segmented” compacts made by the compaction of the powder in small equal successive in(1) J. H.Petropoulos and P. P. Roussis, J. Chem. Phys., 47, 1491 (1967). (2) J. H. Petropoulos and P. P. Roussis, J. Chem. Phys., 47, 1496 (1967). (3) J. H. Petropoulos and P. P. Roussis, J. Chem. Phys., 50, 3951 (1969). ‘ ( 4 )P. P. Rouasis and J. H. Petropoulos,J. Chem. Soc., Faraday Trans. 2, 72, 737 (1976); 73, 1025 (1977). (5) K. Tsimillis and J. H.Petropoulos,J.Phys. Chem., 81, 2185 (1977). (6) C. G. Goetzel, “Treatise on Powder Metallurgy”, Vol. 1, Interscience, New York, 1949, Chapters 8 and 9. (7) ,J. H.Petropoulos and P. P. Roussis, J. Chem. Phys., 48, 4619 (1968). (8) C. N. Satterfield and S. K. Saraf, Ind. Eng. Chem. Fundam., 4,451 (1965). (9) R. M. Barrer and E. Strachan, Proc. R. SOC.London, Ser. A , 231, 50 (1955); R. M. Barrer and T. Gabor, ibid., 251, 353 (1959); 256, 267 (1960); L. A. G. Aylmore and R. M. Barrer, ibid.,290, 477 (1967).
crements. According to one view,’OJ such compacts should be quasi-homogeneous; consequently, the relevant time-lag anomalies are attributable to other causes, namely, to the presence of blind pores. Another view7 is that segmented compacts too may be axially nonhomogeneous. Application of the method of time-lag analysis produced important evidence on this point not obtainable from classical diffusion measurements. Segmented compacts were prepared from graphite powder and ~ h o w nby ~ ,this ~ method to exhibit diffusion behavior characteristic of a macroscopically nonhomogeneous medium (even though one might expect that (i) the low coefficient of friction of graphite would favor homogeneity and (ii) the tendency of the graphite platelets to become oriented normal to the compression axis would favor blind pore formation). In the present paper we carry the method of time-lag analysis further. A series of graphite compacts of the same nominal overall porosity are studied, whose macroscopic structure has been varied systematically by varying the mode of compaction. The nature of their axial structural inhomogeneity is then inferred from time-lag analysis, using N2 as diffusant, and compared with the results of other methods of evaluating variation of local macroscopic structure.
Theoretical Section Application of the method of time-lag analysis requires absorption- and desorption-permeation measurements, in which constant penetrant activities ao, al (ao> al) are maintained at the surfaces of the diffusion barrier a t X = 0 and X = 1, respectively,starting from initial conditions a(X,t=O) = al(absorption) or a(X,t=O) = a. (desorption). For further details and definitions the reader is referred to ref 5. Here we state only that the basic experimental quantities are Js (steady-state permeation flux), La(I) (downstream absorption time lag), Ld(l)(downstream desorption time lag), La(0)(upstream absorption time lag), and Ld(0)(upstream desorption time lag). The time lags may be expressed equivalently as La = La(l),U a La (10) R. Ash, R. W. Baker, and R. M. Barrer, R o c . R. SOC.London, Ser. A , 304, 407 (1969). (11) R. Ash,R. M. Barrer, J. H. Clint, R. J. Dolphin, and C. L. Murray, Philos. Trans. R. SOC.London, 275, 255 (1973).
0022-3654/82/2086-5 128$01.25/0 @ 1982 American
Chemical Society
Diffusion in Nonhomogeneous Solids
The Journal of Physical Chemistry, Vol. 86, No. 26, 1982 5129
TABLE I: Characteristics of Graphite Compacts Studied D E F G“
Plug
method of construction nb 1, cm U,em2 porosity
unsym
sym
unsym
unsym
1
1 0.843 0.790 0.14,
3 0.495 0.799 0.14,
6 0.974 0.799 0.13,
1.193 0.790 0.14,
Constructed by adding three segments to plug F . Number of segments.
La(0), 6L La - Ld(l), and 6 A L ALa - Ld(l) + Ld(0). From these experimental quantities effective diffusion (Dexpt),permeability (Pexpt), and solubility (Sex,,)coefficients may be derived according to the relations
Dexpt= 1 2 / 6 A L Pexpt
(1)
= J d / U ( a o - aJ
(2)
= PexpdDexpt
(3)
Serpt
where 1 is the thickness and U is the cross-sectional area of the plug. For a diffusion system obeying Fick’s law, i.e., characterized by constant S and DT, we simply have DT = Dexpt, S = Sexpt.For a non-Fickian system in which S and DT are functions of X, Dexptand Sexpt define a (virtual) “corresponding Fickian diffusion system” with which the real system may be compared.2 Denoting by subscript s all quantities pertaining to the corresponding Fickian system, the following relations hold: 6L,“ = 2AL; = 26L, = 6AL, = 12/Dexpt
(4)
Comparison of eq 1 and 4 shows that 6 A L = 6AL,. The diffusion behavior of the real system may be conveniently described in terms of the magnitude and algebraic sign of the “non-Fickian time-lag increments” Lha = La - L,B ALha = 6Lh = 6L - 6L,
a”- L,”
(5)
which are determined2 by the function S(X)2DT(X) = S ( X ) P(X). The functional dependence of S and P on X may, in turn, be related to the macroscopic structure of the diffusion medium by means of an appropriate physical model. Such a model suitable for microporous solid-dilute gas systems of the type under consideration here has been presented previously.’ It should be borne in mind, however, that the experimental non-Fickian time-lag increments LEa, ALEa,6LE may, in general, contain contributions from causes other than X dependence of S and DT or P. Thus,2 if P is also a function of time, we expect ALEa = &ha, but, in general, LEa # Lha, 6LE # 6Lh.
Experimental Section The materials used were fine graphite powder (Acheson DAG 621 dispersion powder of specific surface area 70 m2 g-’ and ash content 0.29%) and N2 gas of better than 99.95% purity. Four plugs (D-G) were constructed by compaction of the powder in one ( n = 1)or more (n = 3-6) equal portions between two pistons in a cylindrical die (all made from hardened steel) to a porosity of ca. 0.15 (applied pressure ca.8OOO atm) in the apparatus described previously.4 Their characteristics are given in Table I. In symmetrical compaction both pistons moved nearly symmetricallywith respect to the die.4 In the unsymmetrical mode of compaction, the lower piston was kept fixed with respect to
the die.4i5 Plug G was constructed by adding three more segments to F. After compaction, the die containing the plug was connected to the permeation apparatus described previ~usly.~ The plug surface which had faced the upper piston during compaction was upstream (Le., at X = 0) in the permeation runs (normal or “forward”sense of flow). In one case (plug D), the measurements were repeated after inverting the position of the plug (“reverse”sense of flow) in the manner described previ~usly.~ Absorption-permeation, desorption-permeation, as well as equilibrium sorption measurements were carried out as b e f ~ r e . ~ Additional compacts similar to D-G were also constructed for direct examination of their macroscopic structural inhomogeneity. This was done in two ways: (a) A number of thin pliable Pb or Cd disks of diameter just under the bore of the cylindrical die were inserted in the powder prior to compaction at various positions X and at right angles to the axis. In the case of segmented compacts, the disks were inserted between the segments. The amount of powder contained between successive disks was known. The position of the disks in the final compact was determined by means of a traveling microscope from X-ray photographs taken at right angles to the axis of compression. In this way the mean bulk density of each portion of the compact between successive disks could be estimated without removing the plug from its holder. (b) The information obtained in the above manner was supplemented by observations of X-ray diffraction rings from the 0002 crystal planes of graphite, as described by Bacon.12 In each case, the specimen used was a thin (ca. 2 .mm) slice of the compact representing a longitudinal section along the central axis (made by removing the compact from its holder and grinding it down). It was mounted in the manner specified by Figure l b of ref 12 and transmission photographs taken from various locations using a narrow collimated beam of filtered Cu K a radiation. The integrated optical density of the photographic film across the diffraction ring at the position of maximum blackening (W,J was measured by means of a densitometer.
Results and Discussion Consistency and Reproducibility of the Permeation Measurements. The performance of the permeation apparatus was as described previ~usly,~ except for some temporary unexplained malfunction (which led to rejection of the relevant data) of the capacitative differential pressure gauge (Baratron Type 90 of MKS Instrument Corp.) during the initial period of the work. Permeation runs were in each case repeated by using various values of upstream pressure p o between 20 and 70 torr at a fixed temperature of 296.5 K. No tendency of the permeability or of the time lags to vary systematically with p o was noted and mean values were taken in all cases. Typical examples illustrating the reproducibility of the data are given in Table 11. The values of Sexpt determined through eq 1-3 also showed good reproducibility and no tendency to vary with gas pressure. Furthermore, they agreed satisfactorily with the values determined directly from equilibrium sorption measurements, as shown in Table 111. Time-Lag Analysis. The relevant experimental time-lag data are summarized in Table 111. The values of the observed normalized non-Fickian ~ , 6LE/6L, intime-lag increments LE‘IL;, A L E ~ I A L ,and dicate substantial deviations from normal behavior in all (12) G.E. Bacon, J. Appl. Chem., 6, 477 (1956).
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TABLE 11: Examples of Experimental Permeability (PexDt in cmz s-' X absorp tion-permeation upstream
a
upstream
L
PexDt
L
Pexvt
47.04 27.33 58.75 70.29 35.29 mean
-68 -69 -72 -69 -67 -69
4.8, 4.9, 4.6, 4.8, 4.8, 3.8,
18.,
4.9, 4.9, 4.8, 4.8, 4.8, 4.8,
P O , torr Plug E 46.85 26.95 58.30 69.95 34.90 mean
3.0, 3.0, 3.0, 3.0,
Plug G 57.43 61.61 37.40 mean
N,, 296.5 K.
-213 -217 -210 -213
desorption-permeation
downstream
p o , torr
57.54 61.86 37.78 mean
and Time-Lag (Lin min) Dataa
18., 18., 19.,
18., 18.,
2.9, 3.0, 3.0, 3.0,
58 60 58 59
downstream
L
Pexvt
L
PexPt
17.,
18.,
4.8, 4.8, 5.7z 4.8, 4.8, 4.8,
-76 -72 -75 -75 -76 -75
5.1, 4.8, 4.8; 4.7" 4.7; 4.8,
59 58 56 58
3.0, 2.9, 2.8, 2.9,
-100 -103 -103 -102
3.1, 3.1, 3.1, 3.1,
18., 23., 18., 18.,
Not included in the mean value.
TABLE 111: Experimental Time-Lag Parameters (in min), Solubility Coefficients, and Permeability Coefficients (in em2 s - ' ) for N, at 296.5 K Plug D E F G D*c 80 -88 -456 81 536 168 705 -37 184 -184 -0.31 0.52 2.4, 0.73, 0.72,
18., -75 --69
18., 88 94 181 -11., -3., 3.0 -0.37 -0.03 4.8, 0.74, 0.74,
ll., -19.5 -34., ll., 45.? 31., 77., -1., 7., -7., -0.09 0.19 4.3, 0.82, 0.82,
59 -102 -213 58 272 161 432 -13 56 -55 -0.18 0.26 3.0, 0.87, 0.84,
77 -448 - 94 80 171 525 699 -39 -177 177 -0.33 -0.51 2.3, 0.73, 0.70,
From sorption equilibrium. From permeation measurements. Results of reverse flow runs. a
cases. Furthermore, the latter two quantities obey satisfactorily the relations u E a = -&LE= -U$*= 6LE* where an asterisk superscript denotes quantities pertaining to reverse flow. In accordance with the theoretical analysis of ref 2 and 5, it follows that = U h a , 6LE = 6Lh (although, strictly speaking, LEa = Lha is not proven); i.e., the only identifiable cause of non-Fickian behavior of both singly compacted and segmented plugs is the X dependence of S and DT. Thus, earlier findings4s5are fully confirmed and amplified. In addition to this, we are now in a position to carry time-lag analysis further and to attempt a semiquantitative correlation with the type and extent of axial macroscopic structural nonhomogeneity. In this connection, the following aspects of the data are particularly noteworthy: ( a )Symmetrical us. Unsymmetrical Compaction Mode. The symmetrical mode of compaction should lead to a macroscopic structure (and hence to an S ( X ) P ( X ) function) varying symmetrically about the midsection of the compact (i.e., about X = 1 / 2 ) ; hence, UEa(=6LE)= 0 is As, ~shown in Table 111, plug E satisfies this e~pected.~ requirement; even the small deviation of ALEa(6LE)from zero is attributable to the known4imperfectly symmetrical movement of the pistons during compaction. On the other hand, the marked axial nonhomogeneity of plug E is reflected2in the substantial value of LEa/Lsa.By contrast, the fact that one piston was kept fixed during the construction of plug D should give rise to an S ( X ) P ( X )
x=o
X
=t
Figure 1. Schematic comparative representation of the function S ( X ) P ( X ) in plugs made by (i) slngle compaction (n = 1, line A), (ii) muttiple compaction (n = 5) with identical segments (periodic S ( X ) P ( X ) function, line B), and (iii) multiple compaction (n = 5) with intersegmental variation of the mean segmental S and P (line C).
function highly unsymmetrical about X = 1/2. This is in keeping with the large value of ALEalAL; (whereas LE'IL; is comparable to that for plug E). These findings, incidentally, are fully consistent with earlier analogous results4 obtained with less precise experimental techniques. (b) Single us. Multiple Compaction Mode. Comparison of plugs D ( n = 1)and G ( n = 6 ) is of particular interest with regard to the structural nonhomogeneity of segmented compacts. As already mentioned in the Introduction, one view that has been advancedlO holds that each added segment will be identical with the previous one. Hence, the relevant S ( X )P ( X ) function should be periodic and can be represented schematically by line B in Figure 1, if the corresponding function resulting from the single compaction mode can be similarly represented by line A. According to this view, the magnitude of A.Lha/ALSa and Lha/Lsaof the segmented compact should tend to zero, as n increases, in proportion to l / n and l / n 2 ,re~pective1y.l~ Table 111shows, however, that the values of U E a / h L s a for plug G are only l/z the correspondingvalues for plug D, instead of N ~ as/ required ~ by the periodic S ( X )P ( X ) postulate. Furthermore, comparison of the data for plugs F and G (the latter of which was made by addition of three segments to the former) shows that ALEa/ Usa does not tend to diminish with increasing n. Exactly similar beN
(13) J. H.Petropoulos and P. P. Roussis, J. Chem. Phys., 51, 1332 (1969).
The Journal of Physical Chemistty, Vol. 86, No. 26, 1982 5131
Diffusion in Nonhomogeneous Solids
* 2rI
.=o
5
j _
,
l G 18
1 .o
0 2.2
D
t 8 I I
1.5
:= e D
r;
disc
X =l?
5
Figure 3. Variation of the density of compaction in the axial (vertical) and radial (horizontal) directions in plugs of types D and E (confined in their holders), as estimated from interposed disks.
I
1.6
uI
0.5
1.61 0
1
0.5 V ( X ) cm3
1.5
10
1.5
I
-
I
1.o
I
Figure 2. Axial variation of the cross-sectional mean density of compaction In plugs nominally the same as D-G, as revealed by interposed disks (see text).
havior may be noted in the case of LEa/&' (although, strictly speaking, it is not proven that LEa = Lha!. Thus, the experimental evidence seems to be aganst the periodic S ( X ) P ( X ) hypothesis and in favor of the views of Petropoulos and Roussis,' who pointed out that a gradual change in the conditions of compaction must, in general, be expected, as a segmented compact is built up. Consequently, the mean values of S and P characteristic of a given segment will tend to vary from one segment to the next and the S ( X )P ( X ) function should look like line C in Figure 1 rather than B. This "intersegmental variation" of S and P introduces a term in the expression for u h a / u t (the situation is analogous but a little more complicated in the case of Lh'/Lt) which does not tend to vanish as n increase^.'^ (c) Directional Trend of the Axial Structural Nonhomogeneity. According to the theoretical analysis of ref 2, the algebraic sign of UEa for all unsymmetrical compacts indicates a general tendency of S ( X )P ( X )to decrease with increasing X. The algebraic sign of @ for the symmetrical plug implies that the turning point is a minimum. Hence, S ( X )P(X)tends to assume large (small) values near a plug surface which faces a moving (fixed) piston during compression. The theoretical analysis of ref 7, on the other hand, shows that for penetrant gases of low adsorbability the trend of S ( X )P ( X ) should parallel that of the porosity e(X). Hence, the above findings are consistent with a high (low) degree of compaction in the finished plug near a surface facing a fixed (moving) piston during compression. This is the reverse of what is usually found, e.g., in metal powder compacts which tend to become densified near the moving piston.6 Direct Examination of Macroscopic Structure. In view of the somewhat unusual macroscopic structure of the
graphite compacts deduced from time-lag analysis, more direct information about this question was sought by the methods described in the Experimental Section. The results obtained from compacts constructed similarly but with interposed P b or Cd disks are summarized in Figure 2. In the case of plugs made by compaction in a single step (D, E), the originally flat interposed disks generally became distorted in the finished compact in the manner shown in Figure 3. This indicates that the macroscopic structure is also radially nonhomogeneous.6 In view of this fact, the general trend of the mean crosssectional density of compaction (i.e., the density of compaction averaged over the cross section of the compact) along X is represented in Figure 2 as the plot of the mean density between the ith and (i - 1)th disk against the volume V ( X >between the ith disk and the surface of the plug at X = 0. The precision with which the position of the disks could be determined and the reproducibility of the axial compaction density variation among plugs of nominally identical method of fabrication are also illustrated. The results of Figure 2 fully confirm the conclusion about macroscopic structure drawn from time-lag analysis. The reason for the general tendency of the mean crosssectional degree of compaction to vary along X in a way which is the reverse of that normally observed is undoubtedly to be sought in the unusually low coefficient of friction of graphite. Thus, on one hand, frictional pressure losses along X (which largely determine the axial trend in compaction density) are low;l4 hence, high densification of the powder can be achieved even at locations relatively far away from the moving piston. On the other hand, as confiied by direct monitoring of piston movement," there is significant quasi-elastic recovery of compression strain upon decompression. Measurements with interposed disks indicate that the extent of the said recovery varies according to position along X. Thus, as shown in Figure 4, the outer portions of a symmetrically compacted plug expand upon decompressionmore than the inner ones. In the case of unsymmetrically compacted plugs, recovery takes place largely on the upper (mobile) piston side. The (14) It is remarkable, for example, that admixture of even low proportions of graphite powder can improve substantially the axial uniformity of the density of compaction of other powders (cf. Figure 96 of ref 6).
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The Journal of Physical Chemistty, Vol. 86,No. 26, 7982
Sawakis and Petropoulos
1.15 1.55
1.33
Figure 4. Axial variation of the mean cross-sectional density of compaction in a plug compacted symmetrically in one step after limited (0) and full (0)decompression.
“fixed” piston also recedes to a small extent from the die upon decompression, thus indicating some expansion on this side too. The latter fact explains why the density of compaction usually tends to attain its maximum value at some distance from the fixed-piston end of the compact (cf. Figure 2). The extent to which recovery of compression strain can occur upon decompression should depend on the powder particledie wall friction which obtains in each particular case. This accounts for minor differences in axial compaction density variation (and overall degree of compaction) among plugs of nominally identical construction (cf. Figure 2). The occurrence of further recovery, even a long time after construction of the compact, is also possible, of course, and can account for a noticeable drift in diffusion properties observed in previous work.5 The nature of the distortion of interposed disks in compacts of types D and E is exactly the same as that observed in ceramic and metallic powder compacts and implies similar radial variation of the density of compaction.6 Thus, as shown in the examples of Figure 3, the densification near the fixed-piston end of D tends to be somewhat higher in the center than near the die wall. The reverse is the case near the mobile piston in both D and E. Here the density difference between center and circumference is much more pronounced. In fact, the densification near the die wall is (at all X)close to the maximum to be found anywhere in the plug (thus accounting for the impossibility of achieving a high overall degree of compaction near the mobile piston). The above pattern of two-dimensional compaction density distribution is confirmed by the results of X-ray diffraction measurements performed on longitudinal sections of plugs of types D and E as described in the Experimental section. The values of wd (integrated optical density across the diffraction ring at the position of maximum blackening of the film) at various locations on the central axis and about 2 mm from the circumference are shown in Figure 5. w d is a function of local packing density and degree of orientation in the preferred direction of the crystallites of graphite. A high (low) density of packing would be expected to be associated with a high (low) degree of orientation, because platelike particles can pack most efficiently when parallel to one another. Hence, w d would be expected to vary directly with the local density of compaction and the respective values recorded in Figures 3 and 5 are indeed correlated. This, in turn, implies that (i) removal of the plug from its holder does not materially change its structural pattern and (ii) we may conclude with some confidence from Figure 5 that the detailed structure of plug G differs significantly from that of plug D in that the compaction density near the circumference always tends to be higher than in the center
Figure 5. Variation of the maximum integrated optical density across the diffraction ring, W,, and of the preferred direction of crystallite orientation in the axial (vertical) and radial (horizontal) directions in plugs of types D-G (removed from their holders).
and there is a similar trend with X at both locations. The shape of interposed disks and the position of wd on the relevant diffraction rings also lead to concordant conclusions about the local direction of preferred orientation of the graphite particles. It is perpendicular to the compression axis near the center of the compact but departs from this increasingly near the die wall, as would be expected.I5 The preferred orientation of the particles plays a significant role in determining the local magnitude of DT but does not affect the overall pattern of the S ( X ) P ( X )function deduced from the model of ref 7. Similarly, the fact that radial nonhomogeneity by itself causes no deviation from Fickian time-lag behavior accounts for the present findings that the salient features of the non-Fickian time-lag increments are relatively insensitive to the nature of the detailed two-dimensional macroscopic structure of the diffusion medium.
Conclusion Time-lag analysis has been shown to be a powerful tool for the study of non-Fickian diffusion of penetrants in solid media. The present work emphasizes particularly the potentiality of the method for semiquantitative analysis of diffusion in macroscopically nonhomogeneous solids. The conclusions drawn from the results obtained here are important with reference to the proper way of interpreting non-Fickian diffusion of gases in microporous solids, because they provide further support for the view that the key controlling factor is the macroscopic structural inhomogeneity of the solid rather than the presence of blind pores, even in the case of segmented compacts. In connection with the possibility of obtaining structural information about the solid, it has been shown that the gross axial nonuniformity of the density of compaction can be correctly deduced, as is confirmed by other more direct experimentaltechniques. The latter techniques also reveal a more detailed two-dimensional macroscopic structure, which is too complicated to permit more rigorous quantitative analysis of the time-lag results. However, the fact that time-lag analysis can yield reliable semiquantitative information about overall axial structural nonhomogeneity irrespective of the superimposedradial structural variation is remarkable and of considerable practical value when the method is used as a diagnostic tool. By contrast, transient-state diffusion analysis5may be expected to be more (15) R. E. Nightingale in ‘Nuclear Graphite”,R. E. Nightingale, Ed., Academic Press, New York, 1962, p 106.
J. Phys. Chem. 1982, 86,5133-5135
sensitive to the nature of radial structural nonhomogeneity. Clearly, this opens up further interesting possibilities of obtaining structural information about the diffusion medium, which will be considered in a future paper. Acknowledgment. The present work was sponsored by the Hellenic Atomic Energy Commission and is part of a
5133
Ph.D. Thesis submitted by C.S. to the University of Athens. Thanks are due to the National Research Foundation for a scholarship to C.S., to Professor Th. Yannakopoulos for his active interest and for sponsoring the thesis, to Dr. S. Philipakis for his help with the X-ray diffraction measurements, and to Professor P. Theocaris for making his densitometer available to us.
Electronic Structure of Molecules and Infrared Continua Caused by Intramolecular Hydrogen Bonds with Great Proton Polarizability Bogumli Brrezinski Institute of Chemistry, A. Mickiewicz University, 60-780 Poznafi, Poland
and Georg Zundei' Institute of Physical Chemistry, University of Munich, D8000 Munich 2, West Germany (Received: December 16, 1981)
2-Quinuclidinecarboxylicacid N-oxide (compound 1) and 3-methyl-2-pyridinecarboxylicacid N-oxide (compound 2) are studied by IR and NMR spectroscopy. With both compounds, strong, short intramolecular hydrogen bonds are formed. Both proton-limiting structures OH...ON --t -O.--H+ONhave noticeable weight. Only with compound 1, but not with compound 2, is an intense IR continuum observed. Thus, only if the hydrogen-bond donor and acceptor groupings are not electronically conjugated do IR continua occur, since, when they are conjugated, the charge fluctuation connected with the proton fluctuation is compensated by an electron flux in the opposite direction within the molecule. Thus, not only the proton potential but also the dependence of the dipole moment on the vibrational coordinate of the proton is decisive for the large transition moments and the proton polarizability of hydrogen bonds, and thus for the occurrence of infrared continua. On the basis of these results it is explained that, with a large number of compounds forming intramolecular hydrogen bonds, described in the literature, neither a continuum nor OH or NH stretching vibration bands are observed.
Introduction Various authors1* studied the IR spectra of compounds forming intramolecular hydrogen bonds in which the hydrogen-bond donor and acceptor groupings are electronically conjugated. Perhydroxyquinolines were studied by Josien et a1.l and by Hadii and Sheppard,2hydroxy and ~
~
~~~
~~~~~
(1)M. L. Josien, N. Fuson, J. M. Lebas, and T. M. Gregory, J . Chem. Phys., 21,331 (1953). (2)D.Hadii and N. Sheppard, Trans. Faraday SOC., 50,911(1954). (3)S. Trofimenko, J. Am. Chem. SOC.,85,1357 (1963). (4)K. Hafner, E. A. Kramer, H. Musso, and G. Ploss, Chem. Ber., 97, 2066 (1964). (5)H. L. Ammon and U. Muller. Tetrahedron. 1437 (1974). (6) K. Kuratani, M. Tsuboi, and T. Shimanouchi, B d l . Chem. SOC. Jpn., 25, 250 (1952). (7)B. E. Bryant, J. C. Pariant, and W. C. Fernelius, J . O m . Chem., 19,1884 (1954). (8) W. J. Linn and W. M. Shavkey, J . Am. Chem. SOC., 79,4970(1957). (9)S.Bratan-Mayer and F. Strohbusch, Z.Naturforsch. B , 31, 1106 (1976). (10)M. L. Porte, H. S. Gutowski, and J. Moyer, J. Am. Chem. SOC., 82,5057 (1960). (11)R. Blinc and D. Hadii, J . Chem. SOC., 4536 (1958). (12)A. Bigotto, V. Galosso, and G. Alti, Spectrochim. Acta, Part A, 27,1659 (1971). (13)E.0.Schlemper,C. H. Walter, and S. J. La Placa, J. Chem. Phys., 54,3990 (1971). (14)M. Szafran and B. Brzezinski in "Synthesis, Structure and Properties of Heterocyclic Compounds", W. Wiewi6rowski, Ed., UAM PoznG, 1975,p 219.
0022-3654/82/2086-5133$0 1.2510
amino derivatives of fulvenes by T r ~ f i m e n k oby , ~ Hafner et and by Ammon and Muller,5 hydroxy and amino derivatives of tropolenes by Kuratani et al.? by Bryant et al.,7 and by Linn and Shavkey; and rubazonic acid by Bratan-Mayer and S t r o h b u ~ c h . ~With all these compounds, with which the hydrogen-bond donor and acceptor groupings are electronically conjugated, no continuum or bands due to OH or NH stretching vibrations could be observed. Only with a very large layer thickness was a weak increase of the background in the region below 3000 cm-', compared with deuterated compounds, found. Compounds forming intramolecular hydrogen bonds in which the hydrogen-bond donor and acceptor groupings are partially electronically conjugated, i.e., in which the electronic conjugation is limited to a certain degree, were studied in ref 10-15. o-Hydroxy derivatives of benzene compounds were studied by Porte et al.,1° nickel and copper dimethylglyoximates by Blinc and Hadii," by Bigotto et a1.,12 and by Schlemper et al.,13and derivatives of picolinic acid N-oxides by Szafran and Brzezinski.14J5 In all these cases, no band of an OH stretching vibration is observed, but the absorbance of the background below 3000 cm-l is slightly increased. This increase of the absorbance can be recognized by comparison with the spec(15)M. Szafran and B. Brzezinski, Bull. Acad. Pol. Sci., Ser. Sci. Chim., 18,247 (1970);20,735 (1972).
0 1982 American Chemical Society
