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be energetically unfavorable to assume a homogeneous mixture of surfactant ions and nonpolar additives filling up the spherical space. We must, therefore, assume that a substantial part of the solubilizate molecules reside in the center of the micelle which appears to be an aggregate of anthracene derivative molecules surrounded by a surfactant shell. One may regard this as a novel type of an o/w microemulsion in which the anthracenes (although being solids at 25 "C) take the oil part. Rheologically, the systems resemble microemulsions in that they show Newtonian flow behavior, but they differ from those because of their much higher viscosities. Usually the viscosity of a microemulsion is comparable to that of water, which has been ascribed to reversible droplet coale~cence.'~Conversely, the higher viscosities of our systems may indicate a higher aggregate stability as would be expected for anthracene derivative aggregates that are of a pre- or microcrystalline nature as indicated by concentration-dependent features in UV spectra.2 Photoconversion of 90% of the anthracenes causes a large reduction of the macroscopic viscosity while, surprisingly, the aggregate mass is unaffected in the case of the 9-n-butylanthracene and is even increased when the n-pentylanthracene is photodimerized. The aggregate masses and the corresponding viscosities are neither interrelated, nor is there a simple relationship of either quantity to the length of the alkyl chain in the 9-position of the anthracene molecule. We can, therefore, rule out in these cases that the photorheological effects are due to major changes of the size of the entire micelles. Other micellar properties that might contribute to the viscosity of the solutions must change, such as the degree of dissociation and the extent of the electric double layer surrounding the micelles. When the polar 9-anthracenecarboxylic acid is added to CTAB solutions, a completely different situation arises. It had been shown previously for more concentrated solutions (75-250 mM CTAB) that a part of the 9-AC molecules is solubilized in such a way (13) Langevin, D. Acc. Chem. Res. 1988, 21, 255.
that ion pairs of 9-AC anions and cetyltrimethylammonium cations are formed whereby HBr is set free. As a consequence of both the large, strongly binding counterions and the generated electrolyte HBr, long rodlike aggregates are formed that are responsible for the nowNewtonian flow behavior. At the lower concentrations investigated here the observed departure from Newtonian flow has a different cause since many very small and strongly interacting micelles exist in this range. Aggregation is further reduced by photdimerization of the anthracene derivative. Considering the viscosity data, the following microscopic cause of the rheopexy of these solutions emerges: at low shear the viscosity (shear stress 7 divided by shear rate +) is not far from that of water because the small aggregates present behave like dispersed molecules in an ordinary solution. Since the negative slope of the curves KAc/AR vs Ac in Figure 6b reveals attractive interactions of the scattering particles, shearing may induce the growth of aggregates and, at higher shear rates, the formation of larger aggregate structures. Finally, upon further increase of shear rate an equilibrium of buildup and collapse of structures appears as Newtonian flow. Conclusion Static low angle light scattering experiments have revealed that the photodimerization of some nonpolar anthracene derivatives in aqueous micellar solutions of CTAB is accompanied by highly specific changes of micelle sizes and of macroscopic flow behavior. The polar compound 9-anthracenecarboxylic acid can induce the formation of very small micellar aggregates; photodimerization of this compound leads to further shrinkage of the micelles. This smallness of the micelles is the microscopic cause of the rheopectic flow behavior that is already observed at concentrations as low as 20 mM. Registry No. CTAB, 57-09-0; 9-methylanthracene, 779-02-2; 9ethylanthracene,605-83-4;9-n-propylanthracene,1498-77-7;9-n-butylanthracene, 1498-69-7; 9-n-pentylanthracene, 33576-54-4; 9anthracenecarboxylicacid, 723-62-6.
Role of Defects In Radiation Chemistry of Crystalline Organic Materials. 1. ESR Evidence for Electron Trapping in the Mixed Crystals of Binary n-Alkanes at Low Temperatures Hachizo Muto,* Keichi Nunome, Kazumi Toriyama, and Machio Iwasakit Government Industrial Research Institute, Nagoya, Hirate-cho, Kita- ku, Nagoya, 462, Japan (Received: October 5, 1988; In Final Form: January 20, 1989)
An ESR study has been made on the electron stabilization in the mixed crystals of binary n-alkanes irradiated at 77 and 4 K, as the first step in understanding the role of defects in radiation chemistry. Evidence has been obtained to show that the radiation-induced electrons are trapped in the mixed crystals in contrast to the absence of trapped electrons in the neat n-alkanes, together with the following results on the trapping site. The ESR line width (AHml)of trapped electrons (reflecting the effective defect size) correlates with the chain length difference (An,) between two n-alkanes. An increase of Anc gives a higher yield of the trapped electrons probably because of a stabilization due to an expansion of the defect size. The number of defects accessible to the electrons depends on the crystal structures, being slightly larger in triclinic crystal than in orthorhombic crystals. The effect of deuteriation of the molecules on AH,,, in addition to the above results suggests that the trapping site is a crystalline lattice defect created by inhomogeneous contacts of the different chain length molecules at the layer boundary and that preexisting defects such as voids are necessary for electrons to be trapped in crystalline n-alkanes.
Introduction The role of trapped electrons in low-temperature organic solids is a fundamental and important subject in radiation chemistry
of organic materials. A large number of works have been rePorted.'" Almost all of them are performed in glassy solids' or ( 1 ) Narayama, M.; Kevan, L.; Samskog, P.-0.; Lund, A,; Kispert, L. D. J . Chem. Phys. 1984, 81, 2297.
'Deceased. 0022-3654/89/2093-4898$01.50/0
0 1989 American Chemical Society
Electron Trapping in Mixed Crystals of Binary n-Alkanes in crystalline polar compounds.2*3It is believed that the radiation-induced electrons cannot be stabilized in crystalline n-alkanes, which are the most fundamental nonpolar organic compounds. Recently, we have found that the trapped electrons are formed by irradiation of the preirradiated n-alkanes such as eicosane and h e ~ a d e c a n e .This ~ result suggests a creation of trapping defects due to the secondary reaction products produced by the preirradiation. Previously, we detected an ESR signal of trapped electrons in neat n-alkanes irradiated at 77 K,5 though afterward, it was found that the signal was originating from the coexistance of impurities. Ichikawa and Yoshida6 have reported that the radiation-induced electrons are trapped at 77 K in the mixture of 3-methylhexane and n-pentane, which have glassy and crystalline phases in the neat cases, respectively. The result has been interpreted as electrons being trapped in the glassy regions of coaggregated 3-methylhexane. The n-alkanes with carbon numbers 6 I nc 5 9 have a triclinic crystal structure, and in the ClO 700 nm. The irradiated sample had no color, suggesting no absorption band in the visible region. From these observations, the species was assigned to be an IR trapped electron. It showed an exponential decay typical to the trapped electron, with a half-life time of about 20 h at 77 K in the dark. The trapped electrons were observed in the mixed crystals of various binary n-alkanes, including the combinations with solute molecular longer than the matrix molecule, as will be described in the later section. The relative yields (Y,) of trapped electrons to the total radical yield depended on the combinations and the relative composition of the two n-alkanes and on the irradiation temperatures. They were in a range of 0.3-3.5% (0.01-0.16 in G value) in most of the samples. These yields are lower than the reported G value in branched alkane glasses (G = 0.3-0.9)14and close to the free-electron yield in liquid n-alkanes (G = 0.1 1-0.18),15 indicating an efficient trapping of the electrons escaped from the geminate recombination. Temperature Effect on AH,,. The main contributor to the ESR line width AH,,,,, of trapped electrons is dipolar hyperfine (1 3) Nunome, K.;Muto, H.; Toriyama, K.; Iwasaki, M. Chem. Phys. Lett. 1976,39, 542. (14)Lin, J.; Tsuji, K.; Williams, F. J . Am. Chem. SOC.1968,90,2766. (15)Fuochi, P. G.;Freeman, G. R. J . Chem. Phys. 1972,56,2323. Dodelet, J. P.; Shinsaka, K.; Kortsh, U.; Freeman, G. R. J . Chem. Phys. 1973, 59,2376.
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TABLE I: Irradiation-Temperature Dependence and Annealing Effect of the ESR Line Width (AH,)
-
of Trapped Electrons (Gauss)
~HlllSl
4 K irrad,
4
4 K obs
4 K obs
G o (1O%)/ClZ
3.4
(5%)/C22 c20 (2%)/C22 C2l (5%)/C22
3.0 3.25
3.3 2.9
4
-
change" of AHml 77 K irrad/ 4 K irrad
77 K /
4 K irrad
Mixed Crystal
c19
c23
77 K irrad, 77 K obs
77 K,
-
5.0 4.7 2.4 2.95
(5%)/C22
3.3 2.8 3.15
0.97 0.97 -
4.5 4.3
0.97
0.93 0.97 0.90
0.91 1.04
CIS(S%)/c21 CI9 (lO%)/C21 c23 (5%0)/c21
-
2.85
-
4.0
-
3.6
-
0.97 0.90
3-meth ylpentane
4.5
3.4
methylcyclohexane 3-methylhexane
5.9
4.3
4.8
3.4
3.4 4.2 3.3
0.76 0.73 0.71
0.76 0.71 0.69
2.5
Glassb
"The ratio of AHmsIis given. bHase, H.; et al. J . Chem. Phys. 1974, 61, 843.
-70
I " ,
,
.
0 2OmolX c10 I100 %)
I
50
,
0
, ' . I 70 100 c12 I
c10 (100% 1
Figure 2. Concentration dependences of the ESR line width AH,,, and mixed crystal irrathe yield Ut, of trapped electrons in CloH22/C,2H2a diated at 77 K .
interactions with neighboring protons.16 Therefore, the change of the width by thermal annealing of the samples is a good measure for the environmental change surrounding the defects.17 The change of AHmlby annealing the samples to 77 K after irradiation at 4 K was measured in several mixed crystals and is listed in Table I. The annealing gave only a 3% decrease of the line width, which is low compared with the reported values of 2530% in glassy solids such as branched alkanes.]' The irradiated temperature dependence of AH,,, was also measured and is listed in Table I. The width AHml of the trapped electrons formed by irradiation at 77 K is not much different from those formed by the irradiation at 4 K. The ratio of AH,,, between the 77 and 4 K irradiations is close to unity [AHmS1(77K)/AHmsI(4K) = 0.9-1.O)J and is different from the reported small values of the ratio in alkane glasses (0.69-0.76)." These results suggest that the electrons in the mixed crystals are trapped in more rigid defects compared with those in glasses and that the neighboring molecules around the defect do not reorient by the annealing or by the irradiation at 7 1 K. Concentration Dependence. The yield ( Yt,) and the ESR line mixed crystals width AHH,, of trapped electrons in CIOH22/C12H26 irradiated at 77 K were measured as a function of the composition side of the of alkanes and plotted in Figure 2. From the CIOHZ2 plot, the yield Yt, increases from 0 to -3.5% as the concentration of the counter alkane (CIZH26) increases to about 10 mol %. At ~~~
~
(16) Iwasaki, M.; Muto, H.; Eda, B.; Nunome, K. J . Chem. Phys. 1972, 56- , 3166 -
_i_l
( I 7) Hase, H.; Warashina, T.; Ogasawara, M.; Higashimura, T. J. Chem. Phys. 1974, 61, 843.
20mol% 50
70
100 c12
Figure 3. Phase diagram of CloH22/C12H26 binary mixture obtained by differential scanning calorimetric measurements. Circles and triangles represent the phase transition temperatures observed.
around a concentration of 10 mol %, the yield drops discontinuously to about a constant value of -2%. The behavior is similar in the case starting from the CI2HZ6 side. The increase of Yctmay be reflecting an increase of the number of defects depending on the solute concentration. The discontinuous changes of yield might suggest an Occurrence of phase transitions. n-Alkanes CZOHd2 and C22H46 have triclinic crystal structures similar to ClOHz2and C12H26, and their binary mixture is known to exhibit phase transitions from the triclinic structure of neat cases to an orthorhombic one.9 A differential scanning calorimetric measurement was made for the C,0/C12mixture. The phase diagram is obtained as shown in Figure 3. It shows that the ClO/Cl2combination has similar phase transitions to the C20/C22combination at around 10 mol % concentration of the counter solute on each side of the two alkanes, supporting the deduction that the observed decreases of Ut, are due to the phase transitions. The concentration dependence of trapped electron yield in the mixed crystals is in marked contrast to the dependence reported for the yield in the 3-methylhexane/n-pentane mixture.6 In the latter mixture, a linear increase of the yield has been observed in the full range of composition of 3-methylhexane. From this result, it has been suggested that the electrons are trapped in the glassy region of the branched alkane. The present result in the mixed crystals of n-alkanes indicates that the number of trapping defects is closely related to the crystal structures and may be suggesting an electron trapping in a crystalline lattice defect rather than in a glassy region. The line width AH,,] of trapped electrons also showed a concentration dependence, though the change was gradual rather than discontinuous in the trapped electron yield. From each side of the two alkanes in Figure 2, as the countersolute concentration
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4901
,
a) orthorhombic
8.
A
/
G- AHmsk
/'
%,I
1
6-
i
4K
b) triclinic
8-
G. AHmst 6-
7
i
;
/' I'
n
-5 c17
-4
4.OG
irra
-3
Cl8 c 1 9
-2
-1
c 2 0 c21
1
r
-3 -2 -1
i
2
%
3
c23 c24 c25
in C2, Figure 4. Dependences of the yield Yt, and the ESR line width AHmsl of trapped electrons on the difference (An,) between the number of carbons of solute and matrix molecules in mixed crystals of binary nalkanes. (a) C2,H4 and (b) CZ2Hd6 are employed as the matrices with orthorhombic and triclinic structures, respectively. Solid and dotted bars represent the observed yield Yteby the 77 and 4 K irradiations, and 0 and 0 represent the observed width AHH,, at the irradiation temperatures, respectively. x indicates the calculated width (see text).
increases, the width AH,,, decreases gradually from about 4 G in both the triclinic regions and levels off to a constant narrow width of -2.5 G in the orthorhombic phase. The decrease of line width might be due to a contribution of defects with larger effective sizes cooperated by two or more solute molecules, in addition to the difference of the effective cavity sizes depending on the crystal structures. Dependence on Chain-Length Difference. The dependences of the yield Ykand the width AH,, on the carbon number difference Anc between solute and matrix molecules were measured and summarized in Figure 4. Long-chain molecules of C Z I H Uand C2ZH46 are chosen as the matrices having orthorhombic and triclinic structures, respectively. This selection was made because the mixtures of short-chain combination such as C7/in C , o with Anc 2 3 had given only a trace amount of trapped electrons. The low yield in the short-chain combinations might be due to a difficulty in making a mixed crystal because of a large difference of the freezing points between the solute and matrix (260 " C ) . In C16-C25/inC2, and Cl,-Cz/in C z binary combinations selected here, the freezing temperature differences are within 3-22 OC. The solute concentration was chosen to be 5 mol % to prevent the phase transitions and to get enough of a S/N ratio of the ESR spectra of trapped electrons in order to estimate the relative yields. It was found that the width AH,,, clearly correlated to the carbon chain difference JAncl,as shown in Figure 4. In the case of orthorhombic matrix (C&), the width AHm, gradually decreases from -5 G and levels off to a constant value of -2.5 G, as IAkl changes from 1 to 4 or 5. The decrease of AH,, is accompanied by an increase of the trapped electron yield Yetat 7 7 K. These Anc dependences resemble each other on both sides with shorter (Anc negative) and longer (Anc positive) solute molecules than the matrix. Since the main contributor to AH,,, is the dipolar hyperfine couplings of protons in the defect wall molecules, the decrease of AH,, corresponds to an increase of the effective defect size. Thus, from these results, it may be reasonably understood that the increase of lAncl makes the effective cavity size larger and results in the increase of the yield, probably because of more stabilization due to an expansion of the size. In the case of triclinic ) in Figure 4b, a similar Anc dependence was crystal ( C Z 2 shown
Figure 5. Change of the ESR spectra of trapped electrons by the deuteriation of the solute and/or matrix molecules in octane (2 mol %)/ decane mixed crystals: (a) CaH18/CIoH22, (b) C8DIS/C10H22, (c) C E H I ~ C I O Dand Z Z(4 , CED~CIODZZ. observed except for a nearly constant yield at 77 K in the shorter solute side. When the irradiation is performed at 4 K, the yield in every mixed crystal seems to approach nearly the same value of 2-3% as a whole, except for the cases of A k = f l in the orthorhombic matrix ( C 2 , ) ,as shown in Figure 4. This result might be that the number of defects is not so much different in every mixture because of the same solute concentration, though the depth of trapping site is different. In the above & = f l cases, no trapped electron is observed at 77 K and only a trace amount is detected even by the irradiation at 4 K. The causes will be discussed later. In addition, there seems to be the following trend. The yield is slightly lower in the orthorhombic matrix than in the triclinic one. This trend and Anc dependence will be discussed later by combination of the crystal structures. Deuteriation Effect on AHms,.The change of ESR line width AHd of trapped electrons by deuteriation of molecules gives useful information on the degree of cooperation of the solute and matrix molecules to the trapping defects. Shown in Figure 5 are the ESR mixed crystals spectra of trapped electrons in c8 (2 mol %)/clo irradiated at 77 K. They showed a decrease of the line width in the order of Cs-h/C,O-h,C8-d/Clo-h,C8-h/Clo-d,and C8-d/Clo-d combinations, giving AHm, = 4.0, 3.0,2.1, and 1.2 G, respectively. The deuteriation of matrix molecule gives a large decrease of AH,, of -2 G. The deuteriation of solute molecule also gives a large decrease of AHmr of about 1 .O G in spite of the low concentration (2 mol %), suggesting that the electron is trapped closely to the solute molecule. The observation of contributions from both molecules indicates that the trapping defects are not in an island composed of aggregated solute molecules but in a boundary region cooperated by the solute and matrix molecules. The deuteriation effect on AH,, was examined also for other mixed crystals with the carbon number difference Anc = -4 to +4. Those results are listed in Table 11. The contributions to the width AH,,, from the proton hyperfine couplings of solute (AHs) and matrix molecule ( A H M )were roughly estimated assuming the following additivity rule AH,,, = AH,,,, + AHs AH, for C s - h / C M - h = AHintr f A H s AHM for C s - d / C M - h = AHintr AH, fAHM for Cs-h/CM-d = AHintr f A H s + f A H M for C s - d / C M - d
+ + +
+ + +
summarized also in Table 11. AHintris an intrinsic line width independent of the hyperfine couplings, and the reducing factor f by deuteriation was derived to be 0.254 from a simulation of the ESR line shape. The ratio AHs/(AHs + A H M )in Table I1 is an estimated fractional contribution from the proton hyperfine couplings of solute to the ESR line width from which the AHintr term in subtracted. The contribution was found to have different Anc dependences in the two cases with shorter and longer solute
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The Journal of Physical Chemistry, Vol. 93, No. 12, 1989
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TABLE 11: Decomposition of the ESR Line Width ( A H , ) of Trapped Electrons to the Contribution of Proton Hyperfine Couplings of the Solute (AHs), the Matrix (AHM),and Independent Term on the Hyperfine Couplings (AHhw)(Gauss) Anc -1
S (2 mol %)/M C9/clO
type of sampleu S
r -2
CS/ClO
S
r av -3 -4 1 2
ClO/CI 2
S
c20/c22 clO/c 13
S
c20/c23
S
clO/c
S
14
S
Cll/ClO c10/c8
S S
r av 3
C12/ClO c13/c10
4
c14/c10
S
S
r S
r
(h/h)
(d/h)
(h/d)
5.4 5.2 4.0 3.9 3.95 4.2 3.7 3.2 3.2 3.6 4.0 3.85 3.85 3.85 3.6 3.3 3.45 3.4 3.35
-
2.6 2.5 2.1 2.0 2.05
3.O 3.O 3.0 3.6 3.2 2.9 3.O 3.3
-
3.3 3.2 3.25 -
-
-
-
2.0 2.2 2.25 2.28 1.8 2.2 2.2 2.1 2.0
(d/d) 1.2 1.3 1.25
-
1.3 1.25 1.28
-
AHint 0.3' 0.3' 0.25 0.41 0.33 0.3' 0.3' 0.3' 0.3' 0.3' 0.4' 0.43 0.38 0.4 0.4' 0.4' 0.4' 0.4' 0.4'
AH, 1.35 1.28 1.27 1.07 1.17 0.8 0.7 0.4 0.3 0.4 0.9 0.97 1.09 1.03 0.8 1.4 1.4 1.25 1.15
AHM 3.75 3.62 2.48 2.41 2.45 3.1 2.7 2.5 2.6 2.9 2.7 2.45 2.38 2.4 2.4 1.5 1.7 1.75 1.8
AHS/ (AHs + AHM) 1/3.7 1/3.8 -1/3 -1/3.2 -1/3.1 1/4.9 1/4.8 1/7.2 1/9.7 1/8.3 -1/4 1/3.5 -1/3.2 1/3.2 1/4.0 -1/2.1 1/2.2 1/2.4 1/2.6
--
------
"s and r are the values for slowly and rapid frozen samples, respectively, and av is their average. 'The same values (0.3 and 0.4) are assumed as in the cases of Cs/Cloand Clo/Cs, respectively.
orthorhombic
triclinic
-+-
I
I
-b
I v I VD DD G Figure 7. Possible packing schemes of molecules in the mixed crystal of binary n-alkanes having orthorhombic structure in the cases with (a) shorter and (b) longer solute molecules (black sticks) than the matrix. V, D, and I indicate the schematic drawing of void, dislocation, and the interweaving of the molecular chain ends without the creations of voids, respectively. DD and VD in (b) show the possible defect and void created by dislocations around the longer solute molecules at the layer boundary.
A A Figure 6. Crystal structures of (a), (b) orthorhombic and (c), (d) triclinic n-alkanes. (b) and (d) are the projections along the molecular chain axis. The areas enclosed by dotted lines show (a), (c) the longitudinal section and (b), (d) the radial section of the cylindrical void expected in the case where the position designated by S is occupied by the solute molecule having shorter chain length by Anc than the matrix one. The void is surrounded by 11 or 10 molecules, of which 6 molecules (drawn by filled circles) are in the radial direction, 1 is the solute S itself, and the other 4 or 3 molecules (Ui-U4) are in the upper layer in triclinic or orthorhombic structures, respectively.
molecules than the matrix one as follows. In the former case (An, negative), there seems to be a crude trend that the solute contribution to the ESR line width [the ratio AHs/(AHs + AHM)] decreases from 1/3-1/4 to -1/9 as lAncl increases from 1 to 4. In the case with longer solute molecule (Anc positive), the contribution does not decrease and rather seems to increase from 1/4 to 1/2.5 as Anc is increased from 1 to 4. The different Anc dependences will be discussed in the next section.
- -
Discussions As candidates for the trapping site of electrons in the mixed crystals, there may be a glassy region, voids, or dislocations. The first one might be less probable because the irradiation temperature
dependence and the annealing effect of AHm1are not as large as that in glassy solids (Table I). The crystal structures of n-alkanes are shown in Figure 6.* The chain end of the molecule designated by S in Figure 6 is surrounded by 11 or 10 molecules in the orthorhombic or triclinic crystals, respectively. Of these, six molecules are in the radial direction, one is the molecule S itself, and the other four or three molecules (U,-U4) are in the upper layer. In an IR study on the mixed crystals of C20H42/C22H46, the creation of voids and the occurrence of gauche form of the chain-end CH3CH2- group of the longer molecule at the layer boundary have been reported in the low-composition regions of the shorter (C20H42) and longer (C22H46) alkanes, respectively.12 Those are designated by V in Figure 7a and G in Figure 7b, respectively. In the middle composition region, it has been suggested that the two kinds of alkane molecules are interleaved at the layer boundary without the creation of voids (I in Figure 7). The present observation of trapped electrons throughout the compositions (Figure 2) and the results on Anc dependence of Yte and AHml(Figure 4) indicate that the Occurrence of a defect cavity accessible to the electrons is not restricted in the low-composition range of the shorter alkane. First, the mixed crystal with a low composition of the solute molecule shorter than the matrix is considered. Suppose the molecule designated by S in Figure 6 was the solute molecule with shorter carbon chain by Anc than the matrix, the void would be expected to be surrounded by the neighboring 11 or 10 molecules and to be a cylindrical cavity with a length correlating to AnC. On the basis of this void model, the Anc dependence of the line width AHmslof the trapped electrons was calculated by an ESR
Electron Trapping in Mixed Crystals of Binary n-Alkanes spectral simulation with the crystal data. The following assumptions were made. The electron locates at the center of the void. The line width is composed from the vertical components of point dipole-dipole hyperfine interactions with the protons (-30 nuclei having the distances of 2.6-5 A) in 11 or 10 cavity wall molecules. The calculated ESR line width rapidly decreases from 8.7 to 3 G as JAncl changes from 1 to 3 and levels off to a constant value of 2.5 G in the region IAncl 1 4, giving a qualitative consistency with the observed trend as shown in Figure 4. From the size of calculated dipolar coupling of protons, the above trend could be understood as follows. The rapid decrease of AHH,,with Anc is due to the increase of distance of the chain-end protons in the solute molecule S itself and in the four (orthorhombic case) to 3 (triclinic case) molecules in the upper layer of the cavity, since those protons have shorter distances from the cavity center than the protons in the six cylindrical wall molecules in the small Anc region. While in the region of IAa-1 beyond 3, their contributions become relatively small and the main contributer is the hyperfine coupling of distant protons in the six cylindrical wall molecules. As a result, the calculation gradually leveled off to a narrower line width. This agreement of trends between the calculation and obervation supports the void model. The calculated values of widths, however, are larger than the observed values in the cases of IAncl = 1-3. One of the causes might be the used point-dipole approximation, which gives an overestimation of the hyperfine couplings for the protons with short distances. The result obtained from the deuteriation, that the solute contribution to AH,,, decreases (1/3-1/4 -1/9) with JAncl(from l to 4), alsosupports the void model as described above, since increasing Anc increases the distance to the cavity center from the protons in the solute molecule located in the longitudinal direction of voids. In the case of Anc = -2 with different binary alkane combinations, however, different solute contributions were estimated in spite of the same Anc [AHs/(AHs + AHM) = -1/3 for Cs/Clo and - 1 / 5 of Clo/Ck2and CzO/Cz2].The cause is not clear. One of the possibilities might be aggregation of the solute molecules, which is different from alkane to alkane. Second, in the case of mixed crystals with a longer solute molecule than the matrix, a similar Anc dependence of the ESR line width (Figure 4) and a different deuteriation effect on AHmk (Table 11) have been observed as found for the shorter solute molecules. The possible defect cavity might be the following. The chain end of the solute molecules with the longer chain length must deform to give a gauche terminal form at the layer boundary as found in the C20H42/C22H46 mixed crystalk2or to shift to the position projected along the molecular-chain axis of the upper layer molecule in Figure 6 in order to be interleaved at the layer boundary. These deformations and shifts might cause dislocations of the neighboring molecules and create a defect cavity or void, designated by DD and VD in Figure 7b, respectively. In the latter void model (VD), the expected effective cavity is considered to be approximately cylindrical with a length correlating to Anc similar to that found for the mixed crystal with shorter solute molecule than the matrix. In the defect model (DD), an increase of A k might also give a larger cavity size, if the deformed terminal part of the longer solute molecule makes a large number of dis-
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The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4903 locations depending on Anc. Both models may be consistent with the observed Anc dependence of AHmk.The latter model (VD), however, cannot explain the observed large contribution from the solute molecule to the ESR line width and its increasing trend [AHs/(AHs AHM) = 1/4-1/2.5] with Anc, since the solute molecule occupies only one position of the six cylindrical wall molecules, which does not make as great a contribution to the line width as the molecule in the longitudinal direction. In the former model (DD), the increasing trend with Anc might be understood as follows. The hyperfine interactions with protons in the solute molecule are expected to increase with Anc if the mismatch of chain lengths makes a cavity with a size correlating to Anc by dislocations around the deformed terminal part (with a length of Anc) of the solute molecule at the layer boundary, as shown in Figure 7b. As is seen in Figure 6, the projected locations of molecules in the lower and the upper layers along the chain axis direction are relatively close to each other in the orthorhombic structure (the location of S is close to that of U,) compared with the locations in the triclinic one. This close location suggests a relatively easy interleaving of the molecules at the layer boundary in the former structure and hence a lower probability of the creation of voids. This causes the relatively lower yields Yet in the orthorhombic crystals, which were observed in the Anc dependences in the two kinds of crystals (Figure 4). The observed very low yield in the Anc = f l cases in orthorhombic CZ1H4 matrix might be due to an easy interleaving expected from the small difference of chain lengths in addition to the above ease originating from the crystal structures. At the present stage, though, it is not easy to specify the defects to quantitatively satisfy all of the observations; the most probable defect accessible to the electrons in the mixed crystals with shorter and longer solute molecules has been suggested to be voids and defect cavities, respectively, created by the inhomogeneous contact of solute and matrix molecules at the layer boundary.
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Conclusion ESR evidence has been obtained that indicates that the radiation-induced electrons are trapped in the preexisting defects in the mixed crystal of binary n-alkanes, in contrast to the absence of trapped electrons in the neat cases. The result suggests that the defect cavity such as a void is necessary for electrons to be stabilized and trapped in the crystalline n-alkanes. The present work also showed that the effective cavity size could be controlled by changing the carbon number difference between the solute and matrix molecules (Anc) and that the binary mixed crystals are useful to study the role of defects in the electron trapping. These mixed crystals are also expected to be of help in understanding the role of defects not only for the electron trapping but also for the radiation-induced reactions concerning radical formations. The investigation in the latter direction is under investigation. Registry No. C8H18,1 1 1-65-9; CloH22,124-18-5; CI2Hz6,112-40-3; C16H34, 544-76-3; C25H52, 629-99-2; C8D18, 17252-77-6;CIOD22, 1641629-8; C2OD42, 62369-67-9; Cl9H40, 629-92-5; C20H42, 112-95-8;C21HMr 629-94-7; C23H4, 638-67-5; C18H38, 593-45-3; C14H30,629-59-4;C9H20, 1 1 1-84-2; Cl3H28, 629-50-5.
