J . Phys. Chem. 1984,88, 3003-3006
3003
Glassy Crystals. 2. Electron Paramagnetic Resonance Study of Molecular Motions and Free Radical Diffusion near the Glass Transition in Cycloalkanols: Evidence for “Chemical” Diffusion Lydia Bonazzola,t Alain H. Fuchs,l Jacques Roncin,+ and Henri SzwarcI* Laboratoire de RPsonance Electronique et Ionique (part of LA 75) and Laboratoire de Chimie Physique des MatPriaux Amorphes (part of LA 75), UniversitP de Paris-Sud, 91405 Orsay, France (Received: July 7, 1983)
Free radicals have been produced by y-irradiation at 77 K in glassy crystalline cycloalkanols and their behaviors as a function of temperature have been studied by EPR spectroscopy. In all cases, the EPR spectrum resolution increases around the glass transition temperature, Tg’,thus revealing the emergence of intramolecular motions in the 107-109-Hzfrequency range. Moreover, free radical recombination, which also begins around Tg’in all cases, has been particularly studied below and above Tg’in cyclooctanol where no recrystallization is feared. 1-Cyclooctanol free radical diffusion, as deduced by using the coagulation model, is several orders of magnitude faster at 150 K than molecular self-diffusion as extrapolated from NMR measurements performed between 253 and 294 K. This shows that radical recombination is ruled by “chemical” diffusion of the free radical centers, all the more so as the activation energy for radical diffusion between 150 and 195 K is almost equal to that for molecular reorientation at 235 K. This is another proof of fast molecular reorientational motions at Tg’ in glassy crystals.
Introduction The present work is to be considered as a part of a more general study of the glass transition, Tg’,in a model system, the glassy crystalline Let us only recall that a glassy crystal is a crystal from the X-ray point of view3v4 that exhibits a glass transition from the thermodynamic viewpoint.’ In a previous paper,5 N M R , stimulated thermocurrents, and thermodynamic measurements yielded data in the 107-1 OW5-Hz frequency domain and disclosed that reorientational molecular motions still occur below Tg’. This demonstrated that investigations at higher frequencies were necessary. This is one reason why the present EPR spectroscopic study was undertaken, as it is well-known that the emergency of molecular motions in the 107-109-Hz range entails modifications in the bandwidths of free radical spectra. For compounds which are not paramagnetic, it is necessary to generate paramagnetic probes within the medium. Spin labeling is currently used for molecular dynamics studies,6 but, when possible, it is preferable to minimize the local perturbations due to the probes; for solid organic compounds, similar to those that give glassy crystals, y-irradiation leads to C-H bond ruptures, producing free radicals. These paramagnetic probes are very similar to the parent molecules that constitute the solid matrix, from which they differ only by the lack of one hydrogen atom. Furthermore, free radicals are known to remain trapped in the same site configurations as the parent molecules7 whenever irradiation temperatures are low enough. Almost 20 years ago, an EPR study on free radicals produced at 77 K in y-irradiated cyclohexanol had shown that, in rapidly cooled samples, part of the free radicals recombined in the 150-200 K temperature range, and that recombination was accompanied by an EPR spectrum band narrowing.8 Since then, Seki and colleagues’ have shown that the above temperature range corresponds to the glass transition of glassy crystalline cyclohexanol ( Tg’ 150 K) followed by recrystallization toward a stable or metastable crystalline phase. We therefore tried to reproduce the above EPR experiment for a y-irradiated cyclohexanol single crystal that had previously been rapidly cooled from 270 to 77 K; such heat treatment is known to yield the glassy crystalline solid.’v4 Figure 1 shows the variation of the number of free radicals as a function of temperature (after -30 min halts at each temperature), together with the relative amplitude of the central line of the corresponding EPR spectrum (that is the amplitude of that band divided by the number of free
-
Laboratoire de RCsonance Electronique et Ionique. *Laboratoire de Chimie Physique des Materiaux Amorphes.
0022-3654/84/2088-3003$01.50/0 -~ , I
,
radicals, which gives a qualitative description of the spectral resolution). It can be seen that the number of free radicals begin to decrease just below Tg’,which could be explained in terms of free radical diffusion, that is in terms of molecular self-diffu~ion.~,~ Furthermore, the change in spectral resolution indicates the emergence of molecular motions in the 107-109-Hz frequency range. Unfortunately, as hinted before, glassy crystalline cyclohexanol recrystallizes in the 160-200 K temperature domain, the exact transformation temperature depending on the sample size and on the previous heat treatment undergone by the studied sample. So we could not be sure that there was not some interference by the recrystallization process in the results that Figure 1 exhibits. It was thus necessary to perform the same experiments for a compound for which no such artefact was to be feared. We had shown that this was the case for cyclooctanol.5 The EPR study was therefore performed on a cyclooctanol batch for which DSC measurements had shown that Tg’was 152 K.’O
-
Experimental Section A -0.2-cm3 polycrystalline cyclooctanol sample was cooled to 77 K and then y-irradiated for 16 h, which corresponds to a total dose of -3.2 X 1020 eV ~ m - ~ . The EPR spectra have been recorded with a Brucker ER-200 D spectrometer from 45 to 195 K. Temperature was varied by a low-temperature Oxford ESR-9 cryostat. The number of free radicals has been determined at 77 K as a function of the absorbed radiation dose by considering that the (1) K. Adachi, H. Suga, and S. Seki, Bull. Chem. SOC.Jpn., 41, 1073 (1968). . ( 2 ) H. Suga and S. Seki, 69th Faraday Discussion, Paper No. 20, Exeter, U.K., 1980. (3) A. Otsubo and T. Sugawara, Sci. Rep. Res. Inst. Tohoku Uniu., A?, 583 (1955). (4) D. Ceccaldi, F. Denoyer, M. Lambert, and H. Szwarc, J . Phys. Lett., 41, L-365 (1980). (5) A. Dworkin, A. H. Fuchs, M. Ghelfenstein, and H. Szwarc, J . Phys. Lett., 43, L-21 (1982). (6) See, for instance, P. Tormala, J . Macromol. Sci. Rev. Macromol. Chem., C17, 297 (1979). (7) D. K . Gosh and D. H. Whiffen, Mol. Phys., 3, 285 (1959). (8) H. Szwarc, J . Chim. Phys., 63, 137 (1966); ThEse de Doctorat, Paris, 1965. (9) R. Marx, J . Chim. Phys., 63, 128 (1966). (10) We thank Drs. A. Dworkin and A. Vassal for purifying cyclooctanol and performing the DSC measurements which were necessary because it was shown that Tg’strongly depends on purity of that compound.
0 1984 American Chemical Society
3004 The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
Bonazzola et al.
E
tz
1
I
I
100
150
I I
T/K
Figure 1. Evolution of the number of free radicals (arbitrary units), 0 , and of the EPR spectrum relative resolution (see text), 0, in a single crystal of cyclohexanol initially y-irradiated at 77 K in the glassy crys-
talline state.
1
1
I
125
175
T/K
Figure 2. Evolution of the final number of 1-cyclooctanol free radicals (arbitrary units) as a function of temperature in cyclooctanol initially y-irradiated at 77 K in the glassy crystalline state.
TABLE I: Initial Number of Free Radicals as a Function of Temperature in Cyclooctanol Initially ?-Irradiated at 77 K in the Glassv Crvstalline Phase ~~~~~
T/K uo/radical cm-3
150 6.4 X 10’8
160 4.2 X
170 180 195 2.6 X 10l8 1.4 X 1OI8 3.8 X 10”
10’8
radiation yield G was equal to 2, which is a sensible value for such a compound.*J’ Afterward, all relative variations of the number of free radicals were calculated with respect to the initial estimated concentration which was 6.4 X 10l8 radicals/cm3. The ratio of the number of free radicals to that of matrix molecules is 1.5 X this can be considered as a large concentration, but it was needed to allow a kinetic study of free radical recombination up to as high a temperature as possible. From 45 to 145 K, the temperature was increased by 15 K steps. In this temperature range, care had to be taken to prevent power saturation. At each temperature, an EPR spectrum was recorded immediately after thermal equilibrium has been reached, then another one was recorded some 20 or 30 min later. No modification in the total free radical number and in the EPR spectrum was observed. At 150 K, four EPR spectra were recorded a t -10-min intervals. A similar procedure was followed at 160, 170, 180, and 195 K. In between, a 15-min interval was considered sufficient to attain temperature equilibrium a t each temperature step. In the 150-200 K range, we no longer had trouble with power saturation.
-
Results Table I shows the initial number yo of free radicals as a function of temperature, that is the number of free radicals corresponding to the first EPR spectrum recorded at 150 K and higher after thermal equilibrium has been established. The final number of free radicals (that is the number corresponding to the last EPR spectrum recorded at a given temperature step) has been plotted as a function of temperature in Figure 2. Tg’has been indicated and, as for cyclohexanol, it can be seen that free radical recombination begins in the vicinity of the glass transition. (Similar curves were also obtained for y-irradiated glassy crystalline cyclopentanol and cycloheptanol.) The variation of the relative free radical concentration as a function of time for different temperature steps is reported in Table 11. It is noticed that the EPR spectrum shape does not change during recombination at a given temperature step. If there had been a significant number of free radical pairs initially trapped at mutual distances less than 40 A, the line widths should have significantly diminished during recombination. (At 40 A, the dipolar contribution of electron spinspin interaction within a pair ~~~
(1 1) “Constantes stlectionntes-Rendements radiolytiques, Tables de Constantes UICPA”, Pergamon Press, New York, 1961.
c
V*
”
Figure 3. Evolution as a function of temperature of the EPR spectrum of 1-cyclooctanol free radicals generated by y-irradiation at 77 K of glassy crystalline cyclooctanol: (a) 150 K; (b) 170 K; (c) 195 K. The deformation of spectrum c, pointed out by the star sign, is due to trapped
electrons produced by y-irradiation of the sample-containing quartz envelope. TABLE I 1 Relative Decrease u,/u2 of the Number qf Free Radicals as a Function of Time and Temperature in Cyclooctanol Initially y-Irradiated at 77 K in the Glassy Crystalline State
at 170K 0.88 0.77 0.74
UI/VO
t/s
-
600 1200 1800 2400
150 K 0.92 0.85
160K 0.94 0.87
0.83
180 K 0.81 0.71 0.60
195 K 0.69 0.56
0.50
0.77
is 1 G.) As this is not the case and as the initial concentration is of the order of it can be assumed that the free radicals are initially randomly distributed. This conclusion will be used later. Figure 3 shows the evolution of the EPR spectrum as a function of temperature. It can be seen that resolution improves as the temperature increases, as in cyclohexanol. A similar improvement has been observed in cyclopentanol and cycloheptanol. This spectrum can be understood in terms of a triplet of triplets of bands. This was to be expected, because, for irradiated solid
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3005
Glassy Crystals TABLE III: Free Radical Recombination Frequency Factor, a, Free Radical Diffusion Coefficient, DEPR, and Extrapolated Self-Diffusion in Cyclooctanol Initially y-Irradiated at 77 K in Coefficient, DNMR, the Glassy Crystalline Phase“ DEpR/CmZ S--I DNMR/cm2S-’ a/s-l %R TIK 150 160 170 180 195 a
R=
0.55 X 0.65 X
1.46 1.52
0.80 X
1.81
1.50 X 2.55 X
1.43 3.15
1.4 2.5 5.5 1.8 1.1
X X 1O-I’ X lo-’’ X X
5.8 X 1.0 X lo-’’ 1.2 X 10-l’ 1.2 X 2.2 X
[E(aeXpt - ath,,)Z/n]’/Z, where n is the number of experimen-
tal points.
alcohols, the trapped free radical is derived from the parent molecule by the removal of the hydrogen atom which was initially bonded to the carbon atom that bears the O H Thus, the unpaired electron interacts with two pairs of equivalent pprotons, which leads to the observed spectrum. Determination of the Free Radical Diffusion Coefficient. Our working hypothesis was that the free radicals recombine whenever they come sufficiently close to one another after diffusing through the solid matrix. We will define below how close is “sufficiently close”. In order to determine diffusion coefficients as a function of temperature, we chose to use the coagulation model such as reviewed by Chandra~ekhar’~ (the pertinent equation-eq 463and figure-Figure 9-are reported on p 63 of ref 13) because of the striking analogy between that model and the present situation; here, we assume that free radicals, initially randomly distributed, disappear each time they encounter (we will examine that point in the discussion) and that the proportion of recombining free radicals within the experimental time interval at each temperature step does not exceed the values at which the relevant equation would cease to be valid because of three- (or more) particle coagulation. According to the previous model, the relative evolution of the free radical concentration can be represented by 1
VI _ --
vo
(1
+ VOT)2
-(1
1
+ at)2
(1)
where vo is the initial measured concentration at the considered temperature step, v I is the free radical concentration as a function of time t, with T
= 4irDt
hence a = 4av4R
D is the diffusion coefficient and R is the radius of the interaction sphere within which free radicals are “sufficiently close” to recombine; R was assumed to equal 5 A, which means that we considered that the van der Waals envelopes of the interacting free radicals must almost touch to allow “coagulation”. a, which can be considered to be a frequency factor, has been determined by least-squares fitting of the experimental data to eq 1. The variations of a and D (which we will call DE,,) as a function of temperature are reported in Table 111. From the variation of DE,, vs. 1/T, the activation energy for free radical diffusion can be estimated as 3.7 f 0.8 kcal mol-I, so that DEpR = 3
X lo-’,
exp(-3700/RT) cm2 s-I
Discussion Two different mechanisms can be called upon to explain free radical diffusion. The first would consist of site-to-site free radical jumping, which is equivalent to matrix molecule self-diffusion. (12) T. Ohmae, S. I. Ohnishi, H. Sakurai, and I . Nitta, J . Chem. Phys.,
42, 4053 (1965).
(13) S . Chandrasekhar, Reu. Mod. Phys., 15, 1 (1943).
We will call it “physical diffusion”. In the second process, free radicals would react with the next molecule by abstracting a hydrogen atom, thus propagation the free radical entity to a neighboring site. We will call it “chemical diffusion”. Because of the different C H bond energies (the bonding energy of the a-hydrogen of the carbon bearing the O H group is generally 8-10 kcal lower than that of a corresponding (?-hydrogen atomI4), a 1-cyclooctanolfree radical would only abstract the H atom bonded to the C atom of the C H O H group of cyclooctanol. Obviously, for this process to be efficient, it is necessary that free radicals and matrix molecules undergo large angle reorientations similar to those that occur in the so-called plastic phase. These reorientations are also necessary for 2 neighboring free radicals to recombine whatever the diffusion process is. In order to discriminate between these two mechanisms, we will extrapolate to 150 K dynamic data derived from 30-MHz NMR measurements performed between 253 and 294 K in the plastic phase, I, of cyclooctanol.15 It is to be stressed that, above Tg’, we are still dealing with phase I, even if it is in a metastable state. This is the reason why we feel it is legitimate to extrapolate values which were determined close to the melting temperature range. Only the accuracy will be questionable. The correlation time for diffusion, Tdiff, was derived from transverse relaxation time, T,, and dipolar energy relaxation time, TD, determinations. Using the Slichter-Ailion strong collision model16 for TD and the Torrey model” of isotropic jumps of length 1 for T2,these two independent series of measurements lead to coherent data, that is, for instance
.#“
=” - 2.4 X
~DNMR
s at 294 K
1 was calculated by assuming that the cyclooctanol crystal structure is fcc as is that of cyclohexanol (space group Fm3m, Z = 4).20 Each molecule is surrounded by 12 neighbors lying a t 1 = a/21/z (a is the crystalline unit cell parameter) with a = 9.56 A as derived from the density at 293 KeZ1 Using the relationship
we get Do = 0.4 cm2 s-l and Eo = 13.6 kcal mol-’, which are typical of values for self-diffusion in plastic crysta1s.l8 Extrapolating the above data to 150 K leads to values for DNMR that are reported in Table 111, in which they can be compared to D E ~ as R derived from free radical recombination kinetics. It can be seen that, at the lowest temperatures, DEpR is several orders of magnitude higher than the extrapolated values of DNMR, which emphasizes the difference in the activation energies that rule the two series of diffusion coefficients. The experimental inaccuracies and the use of the crude coagulation diffusion model would not explain such differences. It must be concluded that free radical recombination between 150 and 195 K in y-irradiated cyclooctanol is not ruled by physical diffusion. It is to be noticed that DEpR and DNMR would become equal at -200 K, the temperature above which free radical recombination is too fast to be measurable. In regard to chemical diffusion, which remains the only possible mechanism, we already said that it was related to molecular reorientation. Information on this process was drawn from 30(14) V. I. Vedeneyeo, et al., “Bond Energies, Ionization Potentials, and Electron Affinities”, Edward Arnold Ltd., London, 1966. (15) A. H. Fuchs, H. Szwarc, and J. Virlet, to be submitted for publication. (16) D. C. Ailion and C. P. Slichter, Phys. Res. Lett., 12, 168 (19641: phYs. Reu. 4 1371 235 (1965). (17) H. C. Torrey, Phys. Reu., 92, 962 (1953); 96, 960 (1965). (18) N. Boden in “The Plastically Crystalline State”, J. N. Sherwood, Ed., Wilev. Chichester. 1979. D 187. (f9) N. Bloembergen,’E.M. Purcell, and R. V. Pound, Phys. Reu., 73,679 (1948). (20) T. Oda, X-Ray, 4, 2 (1945); 5, 26 (1948). (21) “Handbood of Chemistry and Physics”, 54th ed., CRC Press, Cleveland, 1973-4, p (2-260.
3006 The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 MHz N M R longitudinal relaxation time, TI, measurement^.'^ Applying the usual BPP model’g around the minimum of the TI vs. 1 / T plot, we found the correlation time for reorientation to be T , ~ =, 2.0 X lo-* s at 235 K with an activation energy of E,,, = 3.4 f 0.3 kcal mol-’ for isotropic molecular reorientation. As pointed out by the manuscript’s reviewer, this activation energy could be that of the so-called secondary relaxation almost systematically observed in glassy liquids and glassy crystals. Such a connection between the &relaxation and the molecular reorientation was already suggested by Arndt and Jonas in the case of isopropylbenzene.22 The near equivalence to the DEpR activation energy, 3.7 f 0.8 kcal mol-’, is almost too good. If physical diffusion had not been shown to be impossible, the near equality between E E p R and E, alone would have been convincing support for the chemical diffusion hypothesis. Such a chemical propagation has already been observed in glassy isobutyl iodide matrices to rule the isobutyl to tert-butyl free radical t r a n s f ~ r m a t i o n . ~ ~ Let us now evaluate the correlation time for diffusion as derived from DEPR. We will use the Einstein relationship
with the same value for 1 as before. We will not take thermal contraction into account because we are only looking for orders of magnitude. We find
which is to be compared with the extrapolated value of T , ~ at ~ , ~ , 1.2 X s at 150 K. the same temperature, which is T , ~ = We can write
~f;p/~,,,, = 54.4/1.2
x 10-6 = 4.7 x 107
-
io7
So, a free radical must undergo an average number of lo7 reorientations before reacting with a neighboring molecule. To understand this value, we will examine geometrical and kinetic parameters. By analogy with c y c l ~ h e x a n o leach , ~ ~ cyclooctanol molecular conformer has available 48 orientations per crystalline site, which also should be true for 1-cyclooctanol free radicals. Furthermore, for the propagating reaction to take place, it is necessary for the C-OH groups of the two reacting entities to come into contact, which from the steric hindrance point of view, is the less probable configuration. Even then, the reaction will only be possible when the hydrogen atom in the a-position to the O H group of the molecule is on the same side as the neighboring free radical. In the case of two neighboring 1-cyclooctanol free radicals, this last condition is not required, because the free radical chemical sites are almost planar: any of the two a-orbital halves will lead to the reaction. From the kinetic point of view, the recombination of two free radicals will occur as soon as the molecular orientations are convenient. This is not the case for the free radical-molecule reaction. This reaction is athermal because of the identity of the initial and final
Bonazzola et al. products. But it is necessary that a proton overcome a potential barrier, probably by means of a tunneling process. Moreover, the radical site is planar while the corresponding carbon atom of the molecule is tetrahedral. Thus the reaction has to be assisted by deformation vibrations of both entities, which strongly diminishes the reaction probability. We have no way to evaluate the respective contributions of geometrical and kinetic parameters. We can only make crude guesses based on geometrical considerations. Each pair (free radical adjacent molecule) will occupy (48)2 orientations among which less than 10 (let us say 4) can be reasonably thought to be compatible with reaction. Each radical is surrounded by 12 molecules and we will assign arbitrarily a 1/10 probability to the overcoming of the OH-OH steric hindrance. This leads to a
+
1 48
1 48
-x -x qi2)
1 10
x - = 10-2-10-3
probability for a free radical, at a given crystalline site, to overcome geometrical limitations. This would mean that, once in a convenient orientation, the probability for a 1-cyclooctanol free radical to remove a H atom from the next cyclooctanol molecule is 10-4-10-5. Anyway, it appears that free radical recombination is much easier than free radical-molecule reaction. This means that when two free radicals reach two neighboring crystalline sites, they will almost certainly recombine; this corresponds to the disappearance hypothesis we make when describing the coagulation model. As to the intramolecular motions in the 107-109-Hz range, as disclosed by EPR spectrum resolution improvement, nothing much can be said for the time being. It was impossible to fit the evolution of the spectrum pattern with Lorentzian or Gaussian line shapes. This can be understood in terms of a rapid exchange between the protons in @-positionswith respect to the OH group. This would lead to nonequivalent broadening of EPR lines as a function of their spin states. This problem is under study.
Conclusions The EPR study of free radicals produced at 77 K by y-irradiation of glassy crystalline cycloalkanols, particularly cyclooctanol, has shown the emergence, around the glass transition temperature, Tg’, of intramolecular motions in the 107-109-Hz frequency range; their nature is still unknown. Furthermore, the trapped radicals begin to recombine around Tg’and kinetic studies in cyclooctanol reveals that recombination is ruled by chemical diffusion. This was a surprise for us, because, at the beginning of the present work, we thought it natural that self-diffusion, which is generally very fast in plastic phases, would increase steeply just above Tg’. It can be concluded that free radical recombination is the result of a competition between chemical and physical diffusions; in cyclooctanol, the former mechanism is the leading process, which needs not be true for other compounds. In any event, these results show that, around Tg’, molecular reorientation motions are still potent, which confirms previous N M R result^.^^^^ Registry No. Cyclooctanol, 696-71-9; cyclohexanol, 108-93-0.
(22) E. Arndt and J. Jonas, J . Phys. Chem., 85, 463 (1981). (23) N. Leray and J. Roncin, Int. J . Radiar. Phys. Chem., 4, 347 (1972). (24) D. Andre, D. Ceccaldi, and H. Szwarc, J . Phys., 45, 731 (1984).
(25) T. Eguchi, G. Soda, and H. Chihara, J. Magn. Reson., 23,5 5 (1976).
