1666
J . Phys. Chem. 1989, 93, 1666-1670
maintained for K < 1. For K > 1 the return map becomes noninvertible, and a transition to chaotic motion becomes possible. The experimental map (Figure 7) was constructed to show tongues of similar behaviors, but the structure is different from that of the circle map. Although, the bands of periodic and aperiodic behavior are continuous with changing concentrations, we could not organize the various winding numbers in a coherent structure. This discrepancy is partially due to experimental resolution: certain bands are probably too narrow to be detected. The angular return map (Figure 5 ) , however, already indicates that the circle map cannot serve as a good model: The return map of the quasi-periodic solution is single-valued (as well as invertible); i.e. it is possible to trace the future and past behavior. The return map of chaotic states of the circle map is single-valued but noninvertible; i.e. the past cannot be traced. The return maps of observed chaotic states and probably also of frequency locked states (P8, PIO) are not single-valued. Thus, unlike in eq 5 , e,, is not uniquely determined by On and future behavior cannot be traced. That indicates that two reductions in the dimension of the trajectory, performed by taking a cross section and a return sequence, are still insufficient to uniquely define the system. The dimension of the chaotic attractor must be larger than 3, in agreement with the computation of correlation dimension. The structure of such a system may be revealed by studying the interaction of two difference equations. The lack of an appropriate model inhibits further analysis of the data. The partial similarity to the structure of the circle map, Le. the transition to chaos through quasi-periodic and frequency-locked (complex periodic) states, indicated that the observed structure may be accounted for by interaction of two (or maybe more) oscillators. The source of this interaction may be nonuniform properties (e.g. reactivity) of the wire. Another plausible explanation is spontaneous symmetry breaking of a uniform wire: the local current density (e.g. reactivity) varies then along the
surface, but the average is held constant by the galvanostatic operation. We documented such behavior during periodic and aperiodic motions.22 Another possible source for the complex behavior is a sustained motion between two limit cycles. Two stable cycles are distinct at intermediate concentrations, but their boundary, the generalized Hopf bifurcation, could not be pursued into higher concentration. A mechanism that combines the two cycles, in such a way that the trajectory alternates between them, will account for the loss of two distinct cycles and produce a complex motion that visits them in a regular or chaotic manner. Conclusions This work presents the first coherent two-dimensional diagram of complex dynamic behaviors in a heterogeneous reacting system. The observed structure shows certain similarities with the structure of an oscillator subject to external periodic force (the circle map model). That suggests several mechanisms, such as interaction of oscillators or symmetry breaking, that may account for the complex motions. We showed that electrochemical systems may serve as powerful tools for dynamic experimentation into the transition to chaos and complex dynamics. Despite discrepancies between the forced oscillator (eq 5 ) and our results, the transition to chaos via quasi-periodicity and the complex nature of the two-dimensional map (Figure 7) were demonstrated. A model with two difference equations will probably better resemble our results. Acknowledgment. This work was supported by the US-Israel Binational Science Foundation. Registry No. Ni, 7440-02-0; HISO,, 7664-93-9. (22) Lev, 0.;Sheintuch, M.; Pismen, L. M.; Yarnitski, H. Chem. Eng. Sci., in press.
Behavior of Alkyl Radical Pairs in Urea Channels' H. L. Casal, D. Griller,* R. J. Kolt, F. W. Hartstock, D. M. Northcott, J. M. Park, and D. D. M. Wayner Division of Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada K I A OR6 (Received: October 22, 1987; In Final Form: November 4 . 1988)
Photolysis of single crystals of urea/diacyl peroxide complexes at 10 K gave pairs of alkyl radicals that were separated by two molecules of carbon dioxide. At elevated temperatures the spectra became well-resolved as rotation of the radical centers became fast on the EPR time scale. The maximum resolution of the EPR hyperfine couplings was achieved when the separation between the radicals was greatest. The temperature for the onset of rapid rotation was markedly dependent on the length of the diacyl peroxide. Two radical rearrangements in the urea channels were studied: the cyclopropylmethylring opening and the 5-hexenyl radical cyclization. The former was virtually unaffected by the presence of the urea host while the cyclization of the 5-hexenyl radical showed a marked matrix effect.
Urea is a host material that forms inclusion complexes with a wide variety of roughly linear organic molecules.2 In the presence of suitable substrates, urea crystallizes to form long channels of ca. 5.5-8, diameter and the included molecules are packed lengthwise along them.3 The channels tend to constrain the motion of the included molecules so that they are only capable of rotation about their long axes. In complexes of this kind, interactions between molecules in neighboring channels are fairly insignificant since the urea host completely surrounds the included molecules and keeps them
well-separated. In fact, the interchannel distance in urea inclusion compounds is typically 8.2 A. However, the included molecules can interact with neighboring molecules in the same channel since they tend to butt end to end. We have previously shown that decanoyl peroxide, included in a urea host, gives rise to pairs of nonyl radicals on photolysis that can be detected by electron paramagnetic resonance (EPR) spectroscopy (eq The approach has a number of features
( 1 ) Issued as NRCC Publication No. 29826. (2) Fetterly, L. C. In Non-stoichiometric Compounds; Mandelcorn, L., Ed.; Academic Press: New York, 1960; Chapter 8. (3) Smith, A . E. Acrn Crysrallogr. 1952, 5 , 224.
(4) Casal, H. L.; Griller, D.; Harstock, F. W.; Kolt, R. J.; Northcott, D. J.; Park, J. M.; Wayner, D. D. M. J . Phys. Chem. 1987, 91, 2235. ( 5 ) A similar study has been reported recently by M. D. Hollingsworth and co-workers.6
0022-3654/S9/2093-1666$01.50/0
hv
RCO2CO2R
[R'C02C02R']
Published 1989 by the American Chemical Society
(1)
Behavior of Alkyl Radical Pairs in Urea Channels that yield fascinating insights into the possibilities for movement of molecules that are packed within urea channels4 For example, photolysis yields a radical pair that is separated by two molecules of carbon dioxide and the sudden creation of four fragments from one molecule creates stress within the channel that can drive the radicals apart.' In addition, the zero-field splitting for the radical pair that can be measured by EPR spectroscopy is an extremely sensitive guide to the behavior of the radical pairs, since it is inversely proportional to the cube of the distance separating the radical centers.* In light of these possibilities, we have extended the EPR study to a range of peroxides and have looked at motion as a function of radical size. We have also investigated two radical rearrangements to see how the reaction kinetics are affected by the fact that the radicals were constrained within the confines of the urea channels.
Experimental Section Materials. With one exception, the diacyl peroxides used in this work were prepared by a literature m e t h ~ d . ~Decanoyl peroxide and all of the other materials were commercially available and were used as received. Inclusion Complexes. The following method was used for the preparation of the majority of the peroxide/urea inclusion complexes. A solution of a diacyl peroxide (0.1 g) in methanol (5 mL) was added slowly to a solution of urea (0.5 g) in 2-propanol (25 mL). The complexes crystallized as colorless rods when the solvent was allowed to evaporate slowly. Cyclopropylmethyl and 6-heptenoyl peroxide inclusion complexes were used to study radical rearrangements within the urea channels. These complexes were prepared in a slightly different way so that molecules of decane were included as spacers that separated those of the peroxide. Thus, a hot solution of urea (0.5 g) in 2-propanol (15 mL), methanol ( 5 mL), and decane (4 mL) was mixed with one of the peroxides (0.1 g) in 2-propanol (2 mL). The mixture was rapidly cooled in an ice bath, and the inclusion complex crystallized as small colorless needles. Attempts to produce larger crystals, using slow cooling, led only to a decane inclusion complex that contained insignificant amounts of the peroxide. Instrumentation. The EPR spectrometers used in this work have been described in detail elsewhere.I0 In all cases, radicals were generated by brief photolysis (500-W mercury-xenon lamp) of samples that were located in the spectrometer cavity. Raman spectra were obtained by the irradiation of powdered samples of the complexes using a CR12 argon ion laser (5 145 A; power 150 mW). The scattered light was collected with a computer-controlled Spex 1401 double monochromator that was equipped with a cooled RCA C31034 photomultiplier tube. In all cases, the Raman spectra confirmed that inclusion complexes of the peroxides had been formed since the frequencies of the C-N stretching and N C O skeletal deformation modes were quite different from those for pure urea. This method of analysis has been described in detail el~ewhere.~*l' Results and Discussion In a typical EPR experiment, a single crystal (2-3 mm long) of a diacyl peroxide/urea complex was mounted on a two-circle (6) Hollingsworth, M. D.;Harris, K. D. M.; Jones, W.; Thomas, J. M. J . Inclusion Phenom. 1987, 5, 273. (7) (a) McBride, J. M.; Gisler, M. R. Mol. Cryst. Lig. Cryst. 1979, 52, 425. (b)'Vary, M. W.; McBride, J. M. Ibid. 1979, 52, 4j7. (c) Walter, D. W.; McBride, J. M. J . Am. Chem. SOC.1981, 103, 7069. (d) Ibid. 1981, 103, 7074. (e) McBride, J. M.; Vary, M. W. Tetrohedron 1982, 8, 765. ( f ) McBride, J. M. Acc. Chem. Res. 1983, 16, 304. (8) McBride, J. M. Mol. Cryst. Liq. Cryst. 1983, 96, 19. (h) Hollingsworth, M. D.; McBride, J. M. J . Am. Chem. SOC.1985, 107, 1792. (8) Wertz, J. E.;Bolton, J. R. Electron Spin Resonance. Elementary Theory and Practical Applications; McGraw-Hill: Toronto, 1972. (9) Sheldon, R. A,; Kochi, J. K. J . Am. Chem. SOC.1970, 92, 4395. (IO) (a) Nazran, A. S.; Lee, F. L.; Gabe, E. J.; Lepage, Y . ;Northcott, D. J.; Park, J. M.; Griller, D. J . Phys. Chem. 1984, 88, 5251. (b) Wong, P. C.; Griller, D. J . Org. Chem. 1981, 46, 2327. (11) Casal, H. L. Appl. Spectrosc. 1984, 38, 306.
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1667 TABLE I: Variation of the Zero-Field Splitting Parameter, D , for R'C02C02'R Radical Pairs as a Function of Temperature initial parameters
final parameters
radical
20, G
T;," K
r? 8,
20. G
Ta.' K
r? 8,
butyl pentyl hexyl heptyl octyl nonyld
129 97 107 125 113 115
9.4 7.0 7.5 6.8 6.8 6.3
7.55 8.31 8.04 7.63 7.89 7.85
147 66 72 70 68 61
70 114 130 138 140 155
7.23 9.44 9.17 9.26 9.35 9.69
a Initial photolysis temperature. Distance between radical centers (see text). 'Temperature a t which hyperfine splittings were completely resolved. dReference 4.
TABLE 11: Hyperfine Constants, a", for Alkyl Radical Pairs in Single Crystals of Urea/Diacvl Peroxide ComDlexes at T . radical '/*(aH.)(4H), G '/2(aHs)(4H), G 2 0 , G TRIOK butyl pentyl hexyl heptyl octyl nonylb
11 11 11 11 11 11
14 13.5 14.5 12.5 13.5 13.5
147 66 72 70 68 61
70 114 130 138 140 155
a Temperature at which maximum hyperfine resolution was obtained. *Reference 4.
goniometer that was placed in the variable-temperature probe of the spectrometer. The long axis of the crystal was arranged so that it was parallel with the magnetic field of the instrument. The crystal was then cooled to 7 K and was briefly photolyzed. In all cases, strong and persistent spectra were immediately detected which consisted of two broad lines that were separated by 1OC-130 G (Table I). The spectra were assigned to alkyl radical pairs that were generated on photolysis of the peroxide (eq l), and the separation between the lines was attributed to the dipolar interaction between the radical centers. As we will show, this separation was equal to 2 0 , where D was the zero-field splitting parameter.E The value of D was related to the distance, r, between the radical centers and the spectroscopicgvalueI2and can therefore be a very sensitive probe of the motion within the urea channels (eq 2).
D = (1.39 X 104)g/r3 (G/A3) (2) At 7-9 K the value of D indicated that the average distance between the radical centers was ca. 7.2-8.5 8, (Table I), which is somewhat greater than the separation between the carbon atoms in the peroxide precursor (5.7 A).13 The spectra of the radical pairs showed interesting variations as the temperature was increased to 25 K and above that reflected radical motion within the urea channels. However, Dr. El-Sayed has informed us that a very detailed study of these phenomena has been undertaken by other workers. Following his recommendation, we will refrain from comment on these motions in this paper. At elevated temperatures the spectra showed well-resolved hyperfine splittings indicating that rotation of the radical centers about the long axis of the molecule was fast on the EPR time scale. The temperature for the onset of this resolution, TR, increased with increasing chain length (Table I). At TR all of the spectra had essentially the same value of D that corresponded to a separation of 9.1-9.6 A between the radical centers. As the temperature was increased beyond TR,spectral changes were minimal until temperatures were attained where the radical pairs began to decay (vide infra). Butyl radical pairs behaved quite differently compared to other radical pairs. The TRvalue for these radicals was exceptionally low (70 K), and at temperatures greater than 60 K the radical (12) Eaton, S. S.; Kundalika, M. M.; Bhimrao, M. S.; Eaton, G. R. J . Am. Chem. SOC.1983, 105, 6560. (13) McBride, J. M.; Segmuller, B. E.; Hollingsworth, M. D.; Mills, D. E.;Weber, B. A. Science 1986, 234, 830.
1668 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989
Casal et al. a
a
b
v
,
(Ob
Figure 2. (a) Powder spectrum obtained from the irradiation of a polycrystalline sample of urea/hexanoyl peroxide inclusion complex (T = 193 K). The arrows indicate extra lines which are not expected in a spectrum of a simple monoalkyl radical. (b) Stimulation using aH*(2H)= 21.5 G, aH8(2H) = 27 G , and IJI = 3.5 G (line width = 3.5 G).
Figure 1. EPR spectrum of the heptyl radical pairs obtained from the photolysis of a single crystal of urea/octanoyl peroxide inclusion complex ( T = 138 K): (a) long axis of the crystal aligned parallel to the magnetic field and (b) long axis of the crystal 5 5 O (magic angle) with respect to the magnetic field.
pair spectrum rapidly disappeared leaving an underlying spectrum due to isolated butyl radicals (vide infra). These observations suggest that the butyl radical pairs have far greater mobility within the urea channels than any of their counterparts so that, at relatively low temperatures, they undergo self-reaction leading to the disappearance of the signals. The hyperfine splittings of the radicals were obtained by computer simulation of the spectra. In general, the values obtained were one-half of those observed for the radicals in solution and the multiplicities were twice those for monoradicals as is expected for a strong exchange interaction between two radical centers.* The values of the hyperfine splittings are given in Table 11, and a typical spectrum is shown in Figure la. Thus far, we have proceeded on the assumption that the separation between the main spectral lines was equal to 2 0 where D is the zero-field splitting. However, the proof of the assignment is quite straightforward. It was found that rotation of the long axis of the crystal to the “magic angle”, which is ca. 55’ with respect to the magnetic field, caused the spectrum to collapse to a single line that had double the intensity observed for peaks in the two line spectrum (Figure lb). This observation demonstrates that the original alignment of the crystals (Le., with their long axes parallel to the magnetic field of the spectrometer) was the correct alignment for the measurement of 2D.4 The fact that well-resolved spectra were obtained under certain conditions, i.e., above TR,superficially suggests that the radical centers had considerable freedom of motion above and beyond simple rotation about the long molecular axis. While it may be correct to suppose that the radical centers could bend and rotate fairly freely, this motion was not actually sufficient to produce complete spherical averaging of the hyperfine interaction. In fact, the orientations chosen above for the measurement of the spectra were such that rotations about the long molecular axes would lead to spectra with an isotropic appearance. However, marked anisotropy was revealed when the crystals were rotated so that the long crystal axes were at right angles to the magnetic field. This anisotropy demonstrates that the urea channels do indeed prevent the substantial bending motion of the radical centers that would
be required for complete averaging of the hyperfine interactions. So far, we have limited the discussion to those radical pair systems in which the electron-exchange coupling is strong. In these cases, the spectra observed show hyperfine coupling constants that are one-half of those found in monoradicals and the spin multiplicities that are twice those expected. These spectra were further characterized by an additional coupling which was equal to 2 0 . On prolonged warming at 190 K, the radical pair spectra associated with the butyl, pentyl, and hexyl radical pairs disappeared leaving behind residual spectra (25 8, (eq 2). For the hexyl radical pairs the value of D indicated a separation of 10.4 8, between the radical centers (Table 111). Careful examination of Figure 2 shows that the simulated spectrum does not match perfectly with its ex-
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1669
Behavior of Alkyl Radical Pairs in Urea Channels TABLE 111: Hyperfine Constants, a", Used for Simulation of the Residual Powder Spectra Obtained for Urea/Diacyl Peroxide Adducts after Prolonged Heating radical aHa, G aH5,G IJI", G D, G T, K 21.5 28.5 butylb 0 0 153 21.5 27 3.5 pentyl' 0 193 hexyl cyclopropylmethylb
21.5 21.5
28 28.5
>>lood 0
25
0
173 153
'Value of IJl estimated by spectral simulation (see Appendix). bThe simulation included line broadening due to restricted rotation. No attempt was made to simulate both the effect of electron exchange and broadening line due to restricted rotation (Figure 2). dlJl >> aH.
perimental counterpart. The discrepancy is due to the restricted rotation in the radical which leads to incomplete averaging of the hyperfine interactions due to the @-hydrogens. This has the effect of broadening three of the spectral lines. The phenomenon is not unique to the urea environment and is frequently observed in the spectra of n-alkyl radicals in s01ution.I~ As part of this study of the behavior of radicals in urea channels, we investigated two well-known unimolecular radical rearrangementsI5 to see whether the matrix had an effect on the reaction kinetics. The rearrangements in question were the ring opening of the cyclo.propylcarbiny1 radical and the ring closure of the 5-hexenyl radical. Irradiation of a polycrystalline sample of cyclopropylacetyl peroxide in urea at temperatures as low as 113 K gave only a spectrum of the 3-buten-1-yl radical (eq 3). At this temperature,
6.0
70
80
90
1000/ T ( K )
Figure 3. log ( k ) versus lOOO/T for the cyclization of the 5-hexenyl radical in urea. The line represents the solution data (ref 18) while the points describe the rearrangement in the urea complex.
as was implicit in the monoradical spectra. Indeed, the two experiments suggest that 10-20% of the sites occupied by the smaller radicals allow a significant degree of molecular motion. What is actually most significant about the results for the 5hexenyl radical is that 80% of the radicals failed to undergo cyclization at temperatures where this reaction would have been rapid in solution. The fact that the diameter of the cyclized radical is very close to that for the urea channel must mean that the folding process which leads to cyclizatioli is severely inhibited. Summary
(4)
the radical has a lifetime of ca. 2 s in s ~ l u t i o n . ' ~ We, J ~ therefore, conclude that in the urea channels this rearrangement is not significantly impeded. This result is not unexpected since the channel diameter of 5.5 A is larger than the diameter of the cyclopropyl moiety. In the second investigation, the 5-hexenyl radical (eq 4) was generated by photolysis of a powdered sample of the 6-heptenoyl peroxide/urea complex at 153 K. The initial spectrum was similar to the biradical spectrum obtained in the irradiation of the complex of heptanoyl peroxide. This spectrum disappeared over a period of several minutes, and a new spectrum appearedJhat could only be attributed to a radical of the structure RCH2CHCH2R' (Le., four @-H'swith hfc's of ca. 27 G and 1 a - H with the hfc of ca. 22 G). Apparently, the radical was able to add to the double bond of a neighboring molecule of 6-heptenoyl peroxide. To avoid this problem, we prepared a mixed complex of 6heptenoyl peroxide and decane (molar ratio of 1:50). With this system, we were able to measure the kinetics for the growth of the cyclopentylmethyl radical over the temperature range 108-173 K. At higher temperatures a reaction between the cyclopropylmethyl radical and decane interfered with the kinetic measurements. Careful analysis of the spectra showed that only ca.20% of the total radical population underwent cyclization. The measured rate constants are shown in Figure 3 with the Arrhenius plot for the cyclization reaction in solution.18 The rate constants for the urea complex are ca. 1000 times less than those observed in solution. However, any detailed interpretation of the kinetic results is unwarranted because we are clearly dealing with a matrix site problem. The fact that only a small proportion of the radicals underwent cyclization suggests the existence of defect sites within the channel (14) Krusic, P.J.; Meakin, P.; Jesson, J. P. J . Phys. Chem. 1971, 75, 3438. (15) Griller, D.;Ingold, K. U. Acc. Chem. Res. 1980, 13, 317. (16) Maillard, B.;Forrest, D.; Ingold, K. U. J . Am. Chem. SOC.1976,98, 7024. (17) Mathew, L.;Warkentin, J. J . Am. Chem. SOC. 1986, 108, 7981. (18) Chatgilialoglu, C.; Ingold, K. U.; Scaiano, J . C. J . Am. Chem. SOC. 1981, 103, 1739.
Alkyl radical pairs, generated by photolysis of diacyl peroxide/urea inclusion complexes, were detected by EPR spectroscopy. The average distance between the radical centers was determined from the observed zero-field splitting parameter, D. Maximum resolution of the EPR hyperfine couplings was achieved when the separation between the radicals was greatest. Radical rearrangements in the inclusion complexes could be observed if the products were able to reside within the confines of the urea channel. Thus, the rate of ring opening of the cyclopropylmethyl radical was unaffected when formed in a urea inclusion complex while the ring closure of the 5-hexenyl radical was much slower (ca. 1000 times) than in solution. For the latter, only 20% of all of the radicals were able to cyclize. Acknowledgment. We thank Dr. J. M. McBride for helpful discussions. Appendix The following derivation has been used for the simulation of the biradical spectra. It is essentially a modification of the equations given by Atherton.I9 Consider two radicals I and 11, coupled by J; they have a common g value and hyperfine coupling constants A, and A,, and a total of eight hydrogens, numbered 1 to 8. Hydrogens 1-4 are in radical I and hydrogens 5-8 are in radical 11; hydrogens 1, 2, 5, 6 are a with coupling constants A , and hydrogens 3, 4,7, 8 are @ with constant A,.
i3 i'
R-c-c-
I
H4
I
I
H2
r5 7'
.C-C--R
I
1
H6
I1
If the hyperfine interactions are small enough to be treated to first order, the spin Hamiltonian can be generalized as follows:
(19) Atherton, N.M. In Electron Spin Resonance; Theory and Applications; Ellis Horwood Ltd.: Chichester, 1973.
J . Phys. Chem. 1989, 93. 1670-1673
1670
The Hamiltonian matrix has the following nonzero elements: ( l , + l , M l l , + l , M ) : g@H + Y4J + '/2[Am(Ml
+ M Z + M 5 + M 6 ) + AB(M3
(I,O,MII,O,M):
'/4
(l,-l,MIl,-l,M): -gPH '/z[A,(M, + M2 + M5
+ M 4 + M7 + M 8 ) i
There are four allowed transitions for each set of M i(Le., for a given A(M) and R) with the following intensities (int) 4 2
J
+ '/4J+ M6) + AB(M3 + M4 + M7 +Md1
4
-
2 c.*
(O,O,MIO,O,M): -74J (l,O,MIO,O,M) or (O,O,MIl,O,M): '/2[Aa(MI + M2 - MS - M6)+
+ M4
- M7 -
M8)1
where M I is the eigenvalue of I,, (= for proton), M z is the eigenvalue of IZ2, etc., and M is used as shorthand for the whole set [ M I M M , M 8 ] . If we then define A(M) = j/2[Aa(MI + M Z + M 5 + M 6 ) + + M 4 + M7 + M 8 ) 1
,...
and
3: g@H - YZJ- j/ZR + A(M)
int = (R - 4 / 4 R
+ A(M) 1: g@H + YZJ + Y2R + A(M) 1: g@H + Y z J - Y2R + A(M)
int = ( R
3: g@H - )/2J + j/ZR
In principle there are, therefore, four transitions for each set of nuclear quantum numbers (some of which may be degenerate or very weak). To generate the spectrum, each of the above set of four must be summed over the possible combinations of Mi, i.e. MI =
+Yz,M z = +Yz,..., M7 = +y2, M 8 = +y2
Mi = -'/z,
M I = +'/z,
R = [p
[ A , ( M , 4- M2 - hf~- M6)
Ap(M3
+ M4 - M7 - M8)]2]"2
the following eigenvalues are obtained: E , = g@H Y4J A(M)
+
E2 = -74J E3 = -gPH E4
+
+ '/2R
+ '/4J - A(M)
= -74J - i/zR
+4/4R int = ( R + J ) / 4 R int = (R + 4 / 4 R
hf2 =
+1/2,
Mz = -'/2,
..., M7 = +'/2, M8 =
+'/I
..., M7 = +'/2, M8 = +'/z, ...
Therefore, there are 28 = 256 combinations, but some simplifications are possible since ( M I M 2 ) ,( M , M 6 ) , ( M 3 M4), and (M7 M8) always occur together. In our simulation we have only calculated lines for which the intensity was >1% of the maximum. Registry No. Cyclopropylacetyl peroxide, 55277-81-1;urea, 57-13-6; 3-buten-1-ylradical, 21 54-62-3;cyclopropylmethyl, 2154-76-9; 5-hexenyl radical, 16183-00-9; 6-heptenoyl peroxide, 26841-80-5; cyclopentylmethyl, 23907-66-6;butyl, 2492-36-6; pentyl, 2672-01-7; hexyl, 267929-0; heptyl, 3356-67-0; octyl, 4606-96-6; nonyl, 32757-65-6.
+
+
+
+
Attenuation Lengths of Photoelectrons in Hydrocarbon Films Colin D. Baint and George M. Whitesides* Department of Chemistry, Haruard University, Cambridge, Massachusetts 021 38 (Received: July 5. 1988)
The attenuation length, A, of photoelectrons with energies in the range 900-1400 eV in hydrocarbon films was measured using self-assembled monolayers of alkanethiols, HSC,H2,+,, on gold. The intensity of the photoelectron peaks from the gold substrate decreased exponentially with the chain length, with attenuation lengths of 42 A at 1402 eV, 34 A at 1151 eV, and 28 at 940 eV. Over the narrow energy range studied, X was directly proportional to the kinetic energy of the photoelectrons.
Quantitative analysis of data obtained by X-ray photoelectron spectroscopy (XPS) requires a knowledge of the escape depths of electrons from the surface of a sample.] In order to derive the composition of a homogeneous material from the intensities of the photoelectrons originating from different elements, one needs to know not only the relative atomic cross sections but also the variation of the attenuation length X with the energy of the photoelectrons.2 The ability to derive an elemental depth profile of a layered material from the variation in the photoelectron intensity with the angle of emission requires a knowledge of the absolute value of The recent growth of interest in thin ( < l o nm) organic films4 has generated an immediate need for accurate, reliable values of X in organic materials in general and in thin, densely packed hydrocarbon films in particular. In this paper we have determined the attenuation length of electrons with energies in the range 940-1 400 eV in self-assembled monolayers of n-alkanethiols IBM Pre-Doctoral Fellow in Physical Chemistry 1985-6.
0022-3654/89/2093-1670$01.50/0
(HSC,H2,+,; n = 6, 8, 9, 11, 12, 14, 16, 17, 18, 20, 22) adsorbed on gold. There are two main approaches to obtaining the attenuation length in the surface of a solid. In one technique,, the absolute intensity of an XPS peak from the sample is compared with the signal from a standard, usually gold. Accurate determinations of X require not only that the atomic cross sections in both the sample and the standard, and X in the standard, be known, but also that the two surfaces be free of contamination and that both (1) Briggs, D.; Seah, M. P. Practical Surface Analysis; Wiley: Chichester, 1983. (2) In this paper we will use the terms escape depth and attenuation length interchangeably to mean the thickness of material required to reduce the flux of the emitted photoelectrons by 1/ e and denote both by A. A is not identical with the inelastic mean free path except in the absence of elastic scattering. (3) Bussing, T. D.; Holloway, P. H. J . Vac. Sci. Technol. 1985, A3, 1973. (4) Swalen, J. D., et al. Langmuir 1987, 3, 932. (5) Cadman, P.; Gossedge, G. M.; Scott, J. D. J . Electron Spectrosc. 1978, 13, I . Cadman, P.; Gossedge, G. M. J . Electron Spectrosc. 1980, 18, 161,
0 1989 American Chemical Society
