Molecular Motion in PMMA
The Journal of Physical Chemistry, Vol. 82,
date(1V) complexes that we are currently investigating.
Acknowledgment. We thank Professor A. S. Brill for a listing of the ESR simulation program, CURHEPR, and acknowledge support by NSF Grant No. CHE 76-19571. Supplementary Material Auailable: Tables 1-111 listing the experimental and calculated line width parameters (3 pages). Ordering information is available on any current masthead page. References and Notes (1) L. Barcza and M. T. Pope, J Phys. Chem., 79, 92 (1975). (2) T. Kurucsev, A. M. Sargeson, and B. 0. West, J . Am. Chem. Soc., 61, 1567 (1957); M. T. Pope and L. C. W. Baker, J . Phys. Chem., 63,2083 (1959). (3) L. C. W. Baker and M. T. Pope, J. Am. Chem. Soc.. 82,4176 (1960). (4) M. T. Pope and G. M. Varga, Jr., Inorg. Chem., 5, 1249 (1966). (5) M. T. Pope, S.E. O'Donnell, and R. A. Prados, Proceedings of the XVI International Conference on Coordination Chemistry (Dublin),
No. 26, 1978 2825
1974, paper 3.10; S. E. O'Donnell, Ph.D. Thesis, Georgetown University, 1975. There are two possible substitution sites in a-PzW,,0,,6- illustrated in Figure 1. The subscript 2 identifies the more stable isomer of PzVW,, (R. Contant and J. P. Ciabrini, J. Chem. Res., (5),222 (1977)). I t is not known for certain which of the two kinds of tungsten atoms has been replaced in the a2 isomer. C. M. Flynn, Jr., and M. T. Pope, Inorg. Chem., 12, 1626 (1973). D. P. Smith, H. So, J. Bender, and M. T. Pope, Inorg. Chem., 12, 685 (1973). C. Tourn6 and G. Tourn6, Bull. Soc. Chim. Fr., 1124 (1969). M. M. Ianuzzi, C. P. Kubiak, and P. H. Rieger, J . Phys. Chem., 80, 541 (1976). Program CURKFR (J. H. Venables and A. S. Brill, University of Virginia). R. Wilson and D. Kivelson, J . Chem. Phys., 44, 154 (1966). P. W. Atkins and D. Kiveison, J . Chem. Phys., 44, 169 (1966). J. Hwang, D. Kivelson, and W. Piachy, J . Chem. Phys., 58, 1753 (1973). N. D. Chasteen and M. W. Hanna, J. Phys. Chem., 76, 3951 (1972). As a reviewer has pointed out, at the lower temperatures, T~ is within an order of magnitude close to the breakdown point of the motional narrowing assumption needed to derive eq 2.
Comparison of Molecular Motions Detected by the Spin Label Technique and Carbon-I3 Nuclear Magnetic Resonance in Benzene Solution of Poly(methy1 methacrylate) K. Murakami and J. Sohma" Faculty of Engineering, Hokkaido University, Sapporo 060, Japan (Received March 17, 1978; Revised Manuscript Received October 3, 1978) Publication costs assisted by Hokkaido University
Molecular motions of spin labeled PMMA in benzene solutions were investigated by ESR, and similar motions of nonlabeled PMMA in deuterated benzene solutions were also studied in order to check whether or not the hidden assumption, which is the slight difference of the labeled system from the nonlabeled one, is valid in this system. The rotational correlation times of the polymer side chain as well as their temperature dependences were measured in both systems. Comparison of the correlation times determined by either ESR or 13CNMR indicates that the environment around the label molecule is nearly same as that around the nonlabeled one and the only factor affecting the correlation times is the difference in the molecular size of the foreign group. It was found that the activation energies of the rotational motion of the nitroxide and methoxy group in the side chain were 4.4 and 2.8 kcal/mol, respectively. This unequality is explained again by the difference in the molecular size, that is the smaller activation energy for the smaller group, methoxy, and the larger one for the larger labeling group.
Introduction The spin labeling method has been found useful for elucidation of molecular motion in biological systems,l membranes,2and synthetic polymer^.^-^ Both qualitative and quantitative information on molecular orientation and motion in spin labeled systems has been obtained by analyses of the ESR spectra of the labels. However, implicit in the use of the method is the environmental perturbation caused by the label molecule, however the perturbation is assumed t o be negligible in a spin label experiment. I t is desirable to estimate quantitatively the perturbation due t o labeling and to obtain experimental verification for the negligible perturbation of the label probe to the system. The time factor effective for a change in line widths as well as line shape of ESR spectra from the probe is on the order of 10-9-10-11 s in spin label experiments. It is difficult t o compare the rotational correlation times obtained from a spin label experiment with other data taken from an unlabeled system, because data in this time range for 0022-3654/78/2082-2825$0 1.OO/O
molecular motion in solid systems are seldom available. Correlation times determined by I3C NMR relaxation in high resolution spectroscopy covers a similar range of time, but the application of this technique is limited to the liquid phase. Two experiments, ESR on a spin labeled system and 13C NMR on an unlabeled one, under identical circumstances provide an experimental basis t o determine whether or not the perturbation of the label on the system is negligible.
Experimental Section Samples. Poly(methy1methacrylate) (PMMA), having a nitroxide covalently attached a t the site of the ester side chain (I) was prepared in our laboratory by the method developed by Ohnishi and I t ~ h . 4-Methylacryloxyl~ 2,2,6,6-tetramethylpiperidine(11) was employed as a radical monomer which had been prepared from methacryl chloride and the corresponding hydroxylpiperidine by a method similar to that reported by Kurosaki et alesMethyl methacrylate (MMA) monomers were copolymerized with 1978 American Chemical Society
The Journal of Physical Chemistry, Vo/. 82,
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I
I
0
No. 26, 1978
K. Murakami and J. Sohma
I1
OCH3
I
h'
18
I/
6
Mi=
I
0
1
- 1
Figure 1.
radical monomers by using the conventional method of anionic polymerization. The ratio of ester side chain to the spin labeled one is controlled by the mole ratio of the MMA monomers and radical monomers. The mole ratio of the sample used in this work was taken at 1OO:l. Normal PMMA, nonlabeled samples, for 13C NMR measurements were prepared in our laboratory by the anionic polymerization. The molecular weight of the two kinds of samples, the labeled and the nonlabeled, were approximately same (ca. 8000). The molecular weight was determined by the vapor pressure method. Both samples were isotactic polymers. NMR measurement was carried out for C6D6solution without degassing because it has been shown that oxygen molecules actually exhibit no effect on spin-lattice relaxation times in a polymer s o l u t i ~ n . ~ J ~ A JEOL PE-X ESR spectrometer was used with 100kHz modulation and a temperature control unit attached to the spectrometer was used for temperature variation experiments. 13C NMR spectra were obtained by Bruker S X P spectrometer combined with a probe for high resFigure 2. olution 13C measurement. Temperature variation exTABLE I: I3C Spin-Lattice Relaxation Times ( p s ) at periments were carried out with the attached temperature Various Temperatures control unit.
Results E S R Spectra. The ESR spectra were obtained for the spin labeled PMMA dissolved in benzene in concentrations of 0.0006, 0.003, and 0.015 g/cm3. An example of the spectrum obtained a t 41 "C for the benzene solution (concentration 0.015 g/cm3) of the spin labeled PMMA is shown in Figure 1. The resolved hyperfine splittings appear in each line corresponding to 14N nuclear spin quantum numbers. This pattern is almost same to that reported by Bullock et al.ll for spin labeled PMMA in toluene. The hyperfine splittings, which originate from the coupling with protons in the label molecule and are masked in the broadened spectrum of a solid sample, are now clearly observed. Figure 2 illustrates the temperature variation of the band corresponding to MI = 0 in the spectrum and the resolution of the spectrum increases with increasing temperature. N M R . The proton-decoupled 13CNMR spectra of the nonlabeled PMMA dissolved in deuterated benzene (concentration 0.1 g/cm3) were observed a t various temperatures. Partially relaxed FT spectra of the sample were obtained and the spin-lattice relaxation time T 1of carbons in each group are indicated in Table I. The relative error in this T , measurement was 15%. Determination of the Correlation Times. Correlation Times Determined from ESR Spectra of S p i n Labeled P M M A . The observed spectrum shown in Figure 1 is apparently isotropic except for the line widths which depend on the nuclear magnetic spin quantum number MI. This is the case of complete averaging of the anisotropic g and hyperfine tensors, and the anisotropies of these ESR parameters modulated by isotropic rotational diffusion
2'. "C
CH,
OCH,
C
a-CH,
28 50 65
61 81 189
652 876 1072
747 1296 1450
110 26 7 355
contribute to the line width. According to the Kivelson's theory12 the line width is described by the following equation: Tz(Mj)-' = b2 4 4 T , (6 5M?)-(LyH)' - -bAyHMI 45 15 40
1+
+
where
P
= -hk z z
-
Mgx,
+ gyyN
(3)
H is the applied field, 7, is the rotational correlation time, and T,(MI) is the spin-spin relaxation time, X is the residual line width which is independent of M p One cannot estimate each line widths directly from the observed spectrum because the hyperfine splittings due to the protons are same order of magnitude as the line widths. Computer simulation, in which a line width is taken as a variable parameter, is needed to determine the line width from the observed spectra. A convenient method, however, was adopted for determination of the line widths. One of the multiplets of the spectra, examples of which are shown in Figure 2, was simulated with variable line widths and some of the simulated spectra are shown in Figure 3. The coupling constants used in this simulation were taken as
The Journal of Physical Chemistry, Vol. 82, No.
Molecular Motion in PMMA
26, 1978 2827
8
L I N E W I D T H , gauss Figure 5. Flgure 3.
h;'m
- 10 P
-lc
16'
2.8
3.0
IO?
3.2 T , K-'
34
Figure 0.
TABLE 111: Correlation Times of Each Carbon at Various Temperatures ( T , X 10" s )
Figure 4.
TABLE 11: Hyperfine Coupling Constants ( G ) Due t o the Probe w-CH,(eq) 0.43
S-CH,(eq) 0.48
0-CH,(ax) 0.31
r-H(ax) 0.07
constants and are shown in Table 11. The ratio of the depth of K2 to the peak height K1 in Figure 4 changes sensitively with the variations of the line width, as shown in Figure 3. The changes in the ratio K J K 2 are plotted against the line widths used in the simulation in Figure 5. The tedious computer simulations of the spectra at various temperatures were circumvented by using this curve of Figure 5, and reliable values of the line widths were determined by use of the calibration curve and the observed values of K,/K2 a t each temperature. The line width, estimated in gauss, was converted in T2in seconds on the assumption of Lorentzian line shape. In order to evaluate the correlation time, 7 c ,the spin-spin relaxation times obtained by the above described method were inserted into eq 1 combined with the parameters b and AT, for which g,, = 2.0089, gss = 2.0061, gtZ = 2.0027, All= 32.0 G, and A , = 7.6 G were taken.6 The good linearity in the Arrhenius plot of the correlation times, as shown in Figure 6, provides an activation energy of 4.4 kcal/mol, which is almost independent of the PMMA concentration. Correlation Times Determined from 13CNMR Spectra o f Nonlabeled PMMA. Hatada and co-workers have recently reported that 13C nuclear Overhauser enhancements (NOE) for isotactic and syndiotactic PMMAs is very
T,"C
CH,
OCH,
a-CH,
28 50 65
39.4 31.5 12.7
2.5 1.8 1.5
14.6 6.4 4.5
close to the theoretical maximum value derived from the dipolar mechanism.13 Their NOE results indicate that the spin-lattice relaxation time of 13C is mostly governed by the dipolar interactions with the directly attached prot o n ~ .In~ the ~ extreme narrowing case (w7,
