6038
J . Phys. Chem. 1986,90, 6038-6044
ESR Sptn-Label Study of Poly(methy1 methacrylate) Chain Segment Rotational Dynamics in Dilute Solution J. Pilaf* and J. Labsky Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences, 16206 Prague 6, Czechoslovakia (Received: March 5, 1986; In Final Form: July 7 , 1986)
Dilute solutions of randomly and end spin-labeled poly(methy1methacrylate) (PMMA) were studied in ethyl acetate and dibutyl phthalate solvents in the temperature range 113-373 K. The ESR spectra were analyzed in terms of the axially symmetric rotational diffusion of the spin-label with the rotational diffusion symmetry axis tilted at the angle 0 in the xz plane from the z axis of the spin-label principal axis system of magnetic interaction. All characteristic features of the experimental slow motional ESR spectra were successfully simulated by using a corrected version of the Polnaszeck’s program. Analysis of the temperature dependence of the parameters characterizing the spin-label rotational dynamics leads to a conclusion that the activation energy of the PMMA chain segment rotational diffusion depends on the solvent-dependentheight of the barrier for the local chain motions rather than on the activation energy of the viscous flow of the solvent. A sudden change of this activation energy found in ethyl acetate solvent at about 303 K is probably due to the conformational transition of the PMMA chain observed in a number of solvents at similar temperatures.
Introduction The suitability of ESR spectroscopy for studying spin-label rotational dynamics is well-known.’ Information concerning the rotational dynamics of polymer chain segments may be extracted from ESR studies of spin-labeled polymers? The quality of such information predominantly depends on the degree of understanding of the detailed correspondence between ESR line shapes and spin-label rotational dynamics. We described some of the results obtained in the ESR study of spin-labeled poly(methy1 methacrylate) (PMMA) in an ethyl acetate solvent in our previous paper.2 The nitroxide spin-label is supposed to be bound to the chain segments of this polymer at randomly distributed sites. The ESR spectra of this randomly labeled P M M A ( P M M A I) were analyzed in terms of the an-
-
i
c
PH3- f
- CO-OCH,
J
CO
-50
1
i”‘
A
CN
I OCH,
PMMA
CH2 I -
place, we had to admit the presence of a small amount (about 10%) of the spin-label of higher rotational mobility in the samples to explain the residual differences between the experimental and the “best simulated” slow motional spectra. We ascribed the Occurrence of such -more mobile” spin-label to the presence of a statistically excessive fraction of the end-labeled PMMA molecules formed during copolymerization. To prove this explanation, the end-labeled PMMA (PMMA 11) was synthesised
II
and studied. In the second place, we were not able to analyze properly the low-temperature experimental slow motional spectra in which the center-line splitting had appeared. In this paper we would like to report the results of further studies of both types of spin-labeled PMMA in ethyl acetate and in more viscous dibutyl phthalate solvents.
Experimental Section Spin-Labeled Polymers. The synthesis and characterization
PMMA I
isotropic axially symmetric rotational diffusion of the spin-label characterized by the rotational tensor components R , and RIIand by an angle 0 at which the rotational diffusion symmetry axis is tilted in the x z plane from the z axis of the nitroxide principal axis system of magnetic interaction (below called only “nitroxide axis system”). It was also explained in the paper that an unambiguous complete analysis of the spin-label motional narrowing ESR spectra in terms of the described rotational diffusion model, which means a simultaneous unambiguous determination of all three values of R,, R , and 0, was generally not feasible due to the low amount of information contained in such spectra and that such an analysis might, in principle, be performed only for slow motional spectra. Hence, studies of spin-labeled polymers rotational dynamics should preferably be performed in more viscous solvents. W e have also described two annoying problems encountered in an analysis of slow motional spectra. In the first (1) Spin Labelling Berliner, L. J., Ed.;Academic: New York, Part I, 1976; Part 11, 1979. (2) Pilai, J.; Labskg, J. J . Phys. Chem. 1984, 88, 3659.
of randomly labeled P M M A I has been described earlier.2 The end-labeled P M M A I1 was prepared by the following method. Methyl methacrylate (1 g) was heated to 333 K for 8 h with 0.01 g of 4,4’-azobis(4-~yanopentanoicacid) (Fluka) in acetone (5 mL) under argon atmosphere in a sealed ampule, and P M M A with the carboxyl end group thus formed was precipitated into methanol and dried. The carboxyl end group was changed for the corresponding chloride in a reaction of this polymer (0.2g) with thionyl chloride (0.2 mL), supported by pyridine (0.15 mL) in dried benzene (10 mL) at room temperature. Benzene was evaporated after 24 h, and the polymer was spin-labeled by the acylation reaction with 4-(aminoperdeuterio-2,2,6,6-tetramethylpiperidine-N-oxy13 (0.1 g) in benzene (10 mL) at room temperature. After 24 h the spin-labeled P M M A I1 was reprecipitated 3 times from benzene into methanol and dried. Molecular pa= 4.1l X lo4, rameters of the end-labeled P M M A I1 (nw = 2.58 X lo4 and = 1.59) were determined by GPC and Styragel (Waters, USA) packed columns. The universal calibration principle was employed in the data evaluation. Measurements of ESR Spectra. The spectrometer and other equipment were described earlier.2 All measurements were
nw/M,,
(3) Labskg, J.; Pilai, J.; Lawy,J. J . Mugn. Reson. 1980, 37, 515.
0022-3654/86/2090-6038$01.50/00 1986 American Chemical Society
n,,
Spin-Label Study of Poly(methy1 methacrylate)
a
b
R
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 6039
n
Figure 3. ESR spectrum of PMMA I in ethyl acetate solvent measured at 213 K (-) and simulated spectrum calculated by using parameters R, = 0.006 X IO8 rad s-I, RI1= 1.4 X lo8 rad S-I, and 6 = 51° (---).
r'!
I1,
Figure 1. (a) ESR spectrum of PMMA I in ethyl acetate solvent measured at 253 K (-) and superposition of simulated spectra given in b (- - -). (b) Simulated spectra calculated by using parameters R, = 0.1 X lo8 rad s-I, R1,= 2.4 X IOs rad s-l and 6 = 51' (-) and R, .= 0.2 X lo8 rad s-I, RII = 5.0 X lo8 rad s-l, and 6 = 51' (---). Fraction of
the more mobile spin-label represents 30% of the total spin-label concentration.
Figure 4. ESR spectrum of PMMA I in ethyl acetate solvent measured
at 193 K.
b
n
n Figure 5. ESR spectrum of PMMA I1 in ethyl acetate solvent measured at 193 K (-) and simulated spectrum calculated by using parameters R, = 0.10 X lo8 rad s-', RII = 1.6 X IO8 rad s-l, and 6 = 65' (---).
Figure 2. (a) ESR spectrum of PMMA I in ethyl acetate solvent measured at 233 K (-) and superposition of simulated spectra given in b (---). (b) Simulated spectra calculated by using parameters R, = 0.015 X IO8 rad s-l, Rl1= 2.0 X lo8 rad s-I, and 6 = 51' (-) and R, = 0.1 X lo8 rad s-l, RII= 4.0 X los rad s-I, and 6 = 51' (---). Fraction of
more mobile spin-label represents 20% of the total spin-label concentration. performed at 2-mW microwave output and with 100-kHz magnetic modulation. The polymers were studied in 1 wt % ethyl acetate or dibutyl phthalate solutions in quartz sample tubes of a proper diameter to prevent excessive dielectric loses. All samples were deoxygenated by bubbling nitrogen through a t room temperature before measurement. Both solvents were purified by distillation before use. The activation energy of viscous flow of ethyl acetate (7298 = 0.441 mPa.s, mp 189 K), E,, = 7.8 kJ/mol, was determined by using the tabulated dynamic viscosity data4 in the temperature range 273-348 K. The temperature depen(4) CRC Handbook of Chemistry and Physics,
Raton, FL, 1979.
60th ed.; CRC: Boca
dence of the dibutyl phthalate dynamic viscosity (mp 238 K) may be described by the Vogel-Fulcher expression log 7 = A B / ( T + C) using the values A = -2.04, B = 572, and C = 94.3 in the temperature range 275-403 It follows that the activation energy of the viscous flow of dibutyl phthalate decreases with temperature increasing in this range starting from the value E, = 34 kJ/mol a t 275 K down to 21 kJ/mol at 358 K.
+
Results and Discussion a. Experimental ESR Spectra. As far as the spectra of PMMA I in ethyl acetate solvent discussed in a previous paper2 are concerned, the spectra measured in the temperature range 283-373 K are the typical motional narrowing spectra. The typical slow motional spectra were measured in the temperature range 203-243 K (e.g., Figures 2 and 3) and the spectra measured in the range 253-273 K (e.g., Figure 1) belong to an intermediate region between the two mentioned types. The line shapes of the very slow motional spectra measured at temperatures below 203 K (e.g., Figure 4) approach the rigid limit line shape. The ( 5 ) Stiplnek, P. Ph.D. Thesis, Institute of Macromolecular Chemistry, CzechoslovakAcademy of Sciences, Prague, 1981.
Pilaf and Labsky
6040 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
Y Figure 8. ESR spectrum of PMMA I in dibutyl phthalate solvent measured at 303 K (-) and the simulated spectrum calculated by using parameters R, = 0.006 X lo8 rad s-I, RII= 1.6 X lo8 rad s-l, and 0 = 510 (---).
Figure 6. (a) ESR spectrum of PMMA I in dibutyl phthalate solvent measured at 333 K (-) and superposition of simulated spectra given in b (-- -). (b) Simulated spectra calculated by using parameters R, = 0.06 X 108 rad s-l, RII= 2.2 X lo8 rad s-I, and 0 = 51° (-) and R , = 0.10 X lo8 rad s-I, RI,4.0 X lo8 rad s-l, and 0 = 51’ (- - -), Fraction of more mobile spin-label represents 20% of the total spin-label concentration. R
Figure 9. ESR spectrum of PMMA I in dibutyl phthalate solvent measured at 273 K.
n
Figure 7. ESR spectrum of PMMA I in dibutyl phthalate solvent measured at 323 K (-) and simulated spectrum calculated by using parameters R, = 0.03 X lo8 rad sK1, Rll = 2.0 X lo8 rad s-’, and 0 = 51’ (---).
mentioned center-line splitting is obviously a characteristic feature of the spectra measured at temperatures below 223 K (e.g., Figures 3 and 4). Ethyl acetate solutions of P M M A I1 supplied the motional narrowing spectra within the temperature range 2 13-3 13 K. The spectrum measured a t 193 K (Figure 5) belongs rather to the intermediate region. Below 193 K, the solution starts to solidify and the superposition of slow motional and very slow motional ESR spectra was observed. The expected substantially higher rotational mobility of the spin-label bound to the end chain segment in comparison with the spin-label bound to the inner polymer chain segment follows from this qualitative characterization of the experimental spectra. The experimental P M M A I1 spectra were numerically subtracted from the experimental P M M A I spectra; both were measured in ethyl acetate solvent at the same temperatures in the range 193-273 K. It was found that the P M M A I1 spectra do not form any component of the P M M A I spectra and that the explanation of the origin of the “more mobile” spin-label found in P M M A I samples given in the previous paper* is false. Dibutyl phthalate solutions of P M M A I supplied a motional narrowing ESR spectrum at 373 K, slow motional spectra in the temperature range 303-353 K (e.g., Figures 6-8), and very slow motional spectra a t lower temperatures (e.g., Figure 9). Line shapes of these spectra are similar to those of the spectra of
Figure 10. ESR spectrum of PMMA I1 in dibutyl phthalate solvent measured at 303 K (-) and simulated spectrum calculated by using rotational diffusion parameters R, = 0.3 X lo8 rad s-l, RII= 3.0 X IO8 rad s-I, and 0 = 70° (---).
PMMA I in ethyl acetate solvent measured at temperatures higher by approximately 90 K (cf. Figures 3 and 8). Dibutyl phthalate solutions of P M M A I1 supplied motional narrowing ESR spectra in the temperature range 313-333 K. The spectra measured at 293 and 303 K (Figure 10) belong to the intermediate region. The slow motional spectra were measured in the temperature range 253-283 K (e.g., Figures 1 1 and 12), and very slow motional spectra were measured at lower temperatures (e.g., Figure 13). The center-line splitting also appears in these slow and very slow motional spectra, but their line shapes, including the line shape of the center line, differ from the PMMA I spectra substantially. An inspection of the PMMA I and PMMA I1 spectra measured in dibutyl phthalate solvent a t the same temperatures excludes the idea of the presence of a substantial fraction of the end-labeled P M M A in the P M M A I samples (cf. Figures 8 and 10). b. Simulations of the Slow Motional Spectra. The observed center-line splitting is quite conceivable on the basis of qualitative considerations. Providing that the symmetry axis of the nitroxide anisotropic axially symmetric rotational diffusion is oriented approximately in the direction of the x axis of the nitroxide axis
Spin-Label Study of Poly(methy1 methacrylate)
Figure 11. ESR spectrum of PMMA I1 in dibutyl phthalate solvent measured at 283 K (-) and simulated spectrum calculated by using rotational diffusion parameters R , = 0.06 X lo8 rad s-l, R,, = 1.5 X lo8 rad s-l, and 0 = 65O (---).
Figure 12. ESR spectrum of PMMA I1 in dibutyl phthalate solvent measured at 263 K (-) and simulated spectrum calculated by using rotational diffusion parameters R , = 0.015 X lo8 rad s-’, R,, = 0.8 X lo8 rad s-I, and 6 = 5 7 O (---).
Figure 13. ESR spectrum of PMMA I1 in dibutyl phthalate solvent measured at 243 K.
system, rapid rotational diffusion about this symmetry axis c h a r a c t e d by RIIaverages the positions of the gy and g, extrema in the spectrum and gives origin to the high-field component of the center line, whereas the g, extreme remains resolved due to a slower rotational diffusion about the perpendicular axes characterized by R , and forms the low-field component of the center line. On the other side, attempts to simulate such a line shape of the center line using the original version of the Program for Tilting the Principal Axes of the Magnetic Tensors of a Nitroxide Radical with Respect to the Principal Axis of Diffusion6were quite unsuccessful. It was further found that the line shape of the simulated spectra of the spin-label subjected to the isotropic rotational diffusion and calculated by using this program depends on the orientation of the rotational diffusion symmetry axis. Both of these facts led us to a suspicion that there should be some errors in the program. By comparing the matrix elements calculated in the first step of this program with the wfficients of the original (6) Polnaszek, C. F. Ph.D.
Thesis, Cornell University, Ithaca, NY, 1974.
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 6041 equations: several errors were indeed detected and corrected.’ Then the line shapes of the simulated spectra of the spin-label subjected to the isotropic rotational diffusion calculated by using the corrected version of the program were quite independent of the rotational diffusion symmetry axis orientation. The center-line splitting of the same type as observed in the experimental ESR spectra appears in the simulated slow motional ESR spectra of the nitroxide subjected to the axially symmetric rotational diffusion calculated by using the corrected version of the program and the 8 values ranging from approximately 50’ to 90’. The magnitude of this splitting in the simulated spectra generally increases, with the 0 value increasing in the mentioned range and with R , decreasing. The magnitude of the outer extrema splitting and separation in the simulated spectra generally increases with all three parameters (R,, RII,and 8) decreasing. All the simulated slow motional ESR spectra discussed further in this paper were calculated by using a corrected version of the program, simple Brownian rotation as a model for the spin-label rotational diffusion and A and g tensor components A, = 0.68 mT, A,, = 0.62 mT, A, = 3.41 mT, g, = 2.0103, gy = 2.0065, and g, =, 2.0026, which slightly differ from the values given in the previous paper.2 The line shapes of the simulated spectra proved to be practically insensitive to small differences between the components of the spin-label A and g tensors in ethyl acetate and in dibutyl phthalate solvents determined in the usual manner2 in the analysis of the spin-label rigid limit ESR spectra in both solvents. A very small intrinsic homogenous line width of 0.01 mT was used throughout the calculation. c. Analysis of Experimental ESR Spectra. We started analyzing the slow motional spectra, since a complete and unambiguous analysis of the motional narrowing spectra is generally unfeasible and sensitivity of the very slow motional spectra to the orientation of the rotational diffusion symmetry axis is limited. Center-line splitting and outer extrema separation and splitting in the slow motional ESR spectra of P M M A I in both solvents were successfully simulated by using 8 = 5 1’. This value seems to be determined quite reliably. The center-line splitting changes its character in the simulated spectra when lower 0 values are used. The use of higher 8 values results in an increase in the center-line splitting which must be compensated by increasing R , to fit the experimental shape of the center line. However, such a combination of the rotational diffusion parameters results in the reverse intensity ratio of the components of the center-line splitting and in a simultaneous decrease in the low-field extreme splitting (cf. simulated spectra given in Figures 11 and 12) which are at variance with the experimental P M M A I spectra. The simulated spectra fit satisfactorily experimental P M M A I spectra measured in the ethyl acetate solvent at temperatures below 233 K and the spectra measured in dibutyl phthalate solvent at temperatures below 333 K (e.g., Figures 3 , 7 , and 8). On the other hand, it was quite impossible to simulate simultaneously the intensity ratio of the components of the low-field extreme splitting and the splitting of the high-field extreme observed in the P M M A I spectra measured in ethyl acetate solvent in the temperature range 233-243 K and in dibutyl phthalate solvent at 333 K (e.g., Figures 2 and 6). These spectra may only be analyzed in terms of a two-site model as a superposition of the spectra of “more mobile” and “less mobile” spin-label, similarly to the previous papera2 In the analysis of these spectra, the spectrum of the less mobile spin-label which fits the outer extrema positions and center-line line shape of the experimental spectrum was simulated first. Then the simulated spectrum of the more mobile spin-label was found, the weighted superposition of which (7) In the formula for SY2(K, 2) on p 430 of ref 6, one of the two expressions (XXI+Z.DO) must be deleted. The signs of all the terms which couple to K’= 1 instead of K‘= -1 for K = 1 starting from the CSYM(JJ,K) up to CSYM(JJ + 5, K - 2) on p 447 must be changed. The terms with L’ = Land K ‘ = K + 2 starting from CSYM(JJ, 13) up to CSYM(JJ + 5, 12) on p 449 must not be calculated when simultaneously I = 1 and I I = 1. The signs of the teams which couple to K‘ = 1 K’ = -1 from K = 1 starting from CSYM(JJ, 1) up to CSYM(JJ + 5, 1 ) on p 450 and CSYM(JJ, 4) and CSYM(JJ + 3, 3) on p 451 must be changed.
6042 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
on the simulated spectrum of the less mobile spin-label fitted the experimental spectrum. The fraction of the more mobile spin-label in the samples was determined to be about 30%. Complexity of the described analysis results in a lower accuracy of the rotational diffusion parameters determined particularly as far as the more mobile spin-label is concerned. In an analysis of the very slow motional ESR spectra of PMMA I in both solvents, Rlland R , were only estimated. As the calculation of convergent very slow motional spectra requires extremely long computer time, these estimates are based on fitting only the main features (shape of the center-line and outer extrema separation) of the not completely convergent simulated spectra to the experimental spectra. The relative positions of the lines in the simulated spectra belonging to the intermediate region depend on the 8 value. The fact that the simulated spectra calculated by using 8 determined in the analysis of the slow motional spectra fit the experimental spectra in this respect very well (e.g., Figure 1) confirms its reliability. Problems of a complete analysis of the spectra belonging to the intermediate region are similar to those described in the previous paper2 in connection with the analysis of motional narrowing spectra. In both cases, the All and R , values varying within broad limits fit the line width and/or intensity ratios of the three lines observed in each of the experimental spectra. Moreover, the line shape of the low- and high-field lines in the experimental spectrum measured in the ethyl acetate solvent at 253 K (Figure 1) also indicates the presence of two types of spin-label. This spectrum was analyzed in the same manner as the slow motional spectra in which such superposition occurs. Experimental motional narrowing spectra were analyzed by using the method described previously,2assuming 8 = 51'. This method is not sensitive enough to distinguish whether these experimental spectra are formed by superposition or not. Line shapes of the experimental slow motional spectra of P M M A I1 in dibutyl phthalate solvent, including the character of center-line splitting (e.g., Figures 11 and 12) differ substantially from the PMMA I spectra. The center-line splitting of the same type (as observed in these experimental spectra) appears in the simulated spectra calculated by using 0 values ranging from approximately 60' to 90'. The overall shapes of the P M M A I1 spectra were successfully simulated by using 8 = 70' determined within the mentioned range by fitting the outer extrema separation in the calculated spectra to its value in the experimental spectra. The remaining two parameters which characterize the spin-label rotational diffusion (Rlland R , ) were then determined by fitting the outer extrema splitting and overall line shape of the simulated spectra to the experimental spectra. This analysis revealed a slight decrease of the value of the tilt angle 8 with decreasing temperature down to 57' at 263 K. The PMMA I1 experimental motional narrowing spectra and the spectra belonging to the intermediate region in both solvents (e.g., Figures 5 and 10) were analyzed in the same way as the corresponding P M M A I spectra, provided that 0 = 60'-70'. An analysis of the experimental ESR spectra of both types of P M M A is based on the results obtained in the analysis of slow motional spectra especially as far as the orientation of the rotational diffusion symmetry axes of the spin-label is concerned. The fact that the simulated spectra calculated by using the single site model and simple Brownian rotation as a model for the spin-label rotational diffusion fit most of the experimental slow motional spectra (mainly the low-temperature ones) quite satisfactorially indicates that the application of more sophisticated models of spin-label rotational diffusion is not necessary. We rather believe that the minor residual differences between these experimental spectra and the "best" simulated ones concerning the intensity ratios of spectral components and the relative positions of the center line with respect to the outer extrema may originate in the temperature dependence of A and g tensor components or may be due to the small tilt of the rotational diffusion symmetry axis off the xz plane of the nitroxide axis system. Calculation of the simuIated spectra under the assumption of a quite general orientation of the rotational diffusion symmetry axis which requires
Pilaf and Labsky the introduction of a further parameter has not been performed yet. The two-site model was adopted in the analysis of several experimental slow motional spectra when all attempts to analyze them in terms of modified single site models had failed. The use of the jump diffusion model for the spin-label rotational diffusion or reasonable temperature changes of the A and g tensor components did not improve the fit of the simulated spectra calculated assuming the single site model with these experimental spectra. Any significant distribution of the tilt angles and/or components of the rotational diffusion tensor are not compatible with the sharp extrema observed in the experimental spectra with respect to the strong dependence of the spectral line shapes on these parameters. Results of the described analysis of experimental ESR spectra confirmed the expected difference in the character of rotational diffusion between the spin-label bound to the end segment and the spin-label bound to the inner segment of the PMMA chain. The rotational diffusion of the latter type of the spin-label is supposed to be composed of an approximately isotropic rotational diffusion of the polymer chain segment to which the spin-label is bound, characterized by the rotational diffusion parameter Rs, and of an internal rotation of the spin-label about the chemical bond through which it is bound to the polymer chain segment, characterized by the rotational diffusion parameter RI. Campbell et aL8 showed that such a type of rotational diffusion might be treated within the model of anisotropic axially symmetric rotational diffusion provided that the orientation of the rotational diffusion symmetry axis was identical with the orientation of the axis of chemical bond through which the spin-label was bound to the polymer chain segment, and R , = Rs and RI1= Rs RI. It was explained in the previous paper that practically only the C4-NH bond can contribute to the internal rotation of the spin-label in PMMA I, and it was estimated there,2 from the crystal structure of the bis(2,2,6,6-tetramethyl-4-piperidinyl- 1-oxy)suberate, that the axis of the similar C4-0 bond was tilted at approximately 58' from the z axis in the xz plane of the nitroxide axis system. On the other hand, it was found in the analysis of both series of P M M A I ESR spectra that the orientation of the spin-label rotational difiusion symmetry axis was the same and was temperature independent in both solvents and that this axis was tilted at 5 1' from the z axis approximately in the xz plane. Practical equivalence of the orientation of both axes justifies the application of the suggested spin-label rotational diffusion model and characterization of the spin-label rotational dynamics using the parameters Rs and RI. We find it suitable to note at this moment that another pair of parameters characterizing the spin-label rotational dynamics may be used instead of R , and R,,,e.g., the degree of anisotropy N = R I I / R ,and the correlation time T~ = [6(RllR,)1/2]-1. These parameters, however, supply neither the simple physical picture of the spin-label rotational dynamics nor the straightforward characterization of the polymer segmental dynamics by means of Rs. With respect to the assumed Arrhenius-type temperature dependence of the rotational diffusion tensor components, the parameters Rs and R,determined in the described analysis of the experimenta1 P M M A I ESR spectra measured in ethyl acetate and dibutyl phthalate solvents are given in log R vs. 1/T plots in Figures 14 and 15, respectively. The broad error limits characterize the data determined in the analysis of the motional narrowing spectra and the spectra belonging to the intermediate region in these figures (and in Figures 16 and 17 also). With respect to the mutual dependence of the Rs and RI (and/or R , and Rllvalues, these limits should be understood in such a sense that a particular Rs value from the given limits of Rs determines a particular value of RI from the given limits of RI. Examples of such mutually corresponding Rs and RI values are included in Figures 14 and 15. The data characterizing both the more and less mobile spin-label are given in Figure 14. It was determined in the analysis of a series of PMMA I1 ESR spectra that the rotational diffusion symmetry axis of the spin-label
+
(8) Campbell, R.F.; Meirovitch, E.;Freed, J. H. J . Phys. Chem. 1979,83, 525.
Spin-Label Study of Poly(methy1 methacrylate) 373 353 333 313 293
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The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 6043 T (K1
253
313 293 I !
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213
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lo3
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F i e 14. Arrhenius plots of the rotational diffusion parameters Rs (+) and RI (x) determined in analysis of PMMA I ESR spectra in ethyl acetate solvent. Given values of activation energies were calculated from slopes of full lines. Dashed lines connect data determined from ESR spectra of more mobile spin-label. The symbols 0 and 0 represent examples of mutually corresponding pairs of Rs and R,values.
9-
log R
0-
T[Kl
373 353 333 313 293 273 97Log R
06-
I
30
7-
6-
530
3.5 1/T
lo3
Figure 15. Arrhenius plots of rotational diffusion parameters Rs (+) and R, (x) determined in analysis of PMMA I ESR spectra in dibutyl phthalate solvent. Given values of activation energies E,, were calculated from slopes of full lines. Symbols 0 and 0 represent examples of mutually corresponding pairs of Rs and RI values.
bound at the end of the PMMA chain was tilted at 60’-70’ from the z axis approximately in the xz plane of the nitroxide axis system. In this polymer the spin-label is bound to the end of the
35
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The Journal of Physical Chemistry, Vol. 90, No, 22, 1986
R vs. 1 / T plots in Figures 16 and 17, respectively. The slight decrease of the value of 8 determined in the analysis of the lowtemperature ESR spectra of P M M A I1 measured in dibutyl phthalate solvent (8 approaches 57O at 263 K) may be due to the decrease of the contribution of the mentioned three bonds at the end of the polymer chain to the spin-label rotational diffusion at low temperatures. d. Temperature Dependence of the Rotation Diffusion Parameters. The plots given in Figures 14-1 7 supply log R vs. l / T dependences linear within the limits of experimental error. This finding confirms the assumed Arrhenius temperature dependence of components of the rotational diffusion tensor and makes possible determination of the activation energies of rotational diffusion in particular cases. The plots given in Figure 14 which represent the data determined in the analysis of the PMMA I ESR spectra in ethyl acetate solvent differ from the others by the Occurrence of breaks which divide these plots into two linear parts characterized by different activation energies. Moreover, the low-temperature parts of these plots are split into two lines representing the temperature dependence of the rotational mobility of the more mobile and of the less mobile spin-labels. The presence of both of these types of the spin-label in the sample was proved in the analysis of the experimental spectra measured in the temperature range 233-253 K and cannot be excluded at higher temperatures where the capability of the method to distinguish these two types of the spin-label is limited. The presence of two types of spin-label was also proved in an analysis of the experimental PMMA I spectrum measured in the dibutyl phthalate solvent at 333 K, but there is not enough data available to give a similar splitting of the log R vs. 1 / T plots in Figure 15. Two classes of polymer chain motion are consideredg for a polymer dissolved in a dilute solution: (a) local segmental motion involving only a few neighboring polymer chain segments which is independent of the polymer chain length; (b) rotational diffusion motion of the entire polymer molecule which is strongly dependent on molecular weight and solvent viscosity. These two types of motion compete with each other, but only their resultant is observed. At sufficiently low molecular weights, the rotational diffusion of the entire polymer molecule dominates the relaxation process, and the activation energy of rotational diffusion should give approximately the activation energy of viscous flow of the pure solvent. As the molecular weight of the polymer molecule increases, the activation energy of rotational diffusion should increase also reaching finally its limiting value which represents the barrier for local segmental motions. Results of our experiments indicate a more complicated situation in real dilute solutions. Both low- and high-temperature activation energies of the PMMA segmental rotational diffusion determined in the ethyl acetate solvent (El, = 33 and E,h = 22 kJ/mol, respectively) and also the activation energy determined in the dibutyl phthalate solvent (E, = 60 kJ/mol) are much higher than the activation energies of viscous flow of particular solvents (7.8 kl/mol for ethyl acetate and 20-30 kJ/mol for dibutyl phthalate). This fact suggests that the molecular weight of P M M A I is sufficiently high to prevent the rotational diffusion of the entire PMMA I molecule from playing an important role in the relaxation mechanism. However, the activation energy of PMMA rotational segmental diffusion in the dibutyl phthalate solvent is much higher than the activation energy in the ethyl acetate solvent. Hence, probably some specific P M M A chain segment-solvent interaction affects the barrier for local segmental motions significantly. With respect to the results just mentioned, the only explanation of the observed decrease of the activation energy of P M M A segmental rotational diffusion in the ethyl acetate solvent above 303 K consists in the sudden decrease of the barrier for PMMA local segmental motions in this solvent above this break temperature. Similar conclusions reached Katime et a1.I0 who studied (9) Yang, H. W. H.; Chien, J. C. W. Macromolecules 1978, 11, 759. (10) Katime, I. A,: Garay, M.T.;Francois, J . J . Chem. SOC.,Faraday Trans. 2 1985, 81, 705 and references cited therein.
Pilai and Labsky the molecular weight and temperature dependence of P M M A intrinsic viscosity in a number of solvents, including ethyl acetate. They found that PMMA changes its conformation over the temperature range 318-328 K in this solvent. The common characteristic of this conformational transition is a sudden increase of flexibility of the polymer chain and a decrease of unperturbed dimensions of polymer molecules KOabove this temperature range. They also found that the magnitude of this effect and the transition temperature range depend on the solvent and on the chemical structure and tacticity of the polymer. The existence of such solvent-dependent conformational transitions of the PMMA chain supports the idea forwarded above and regarding the dependence of the barriers for local segmental motions an the solvent. Also, it follows from our experiments that in the temperature range 233-253 K, and probably also in the range 253-303 K just below the break or transition temperature, the PMMA chain may exist in both “more flexible” and “less flexible” conformations in the ethyl acetate solvent. Interpretation of the way in which this conformational transition affects the spin-label internal rotation does not seem to be straightforward. No breaks were found in the log R vs. 1/T plots of the data determined in the analysis of PMMA I ESR spectra in the dibutyl phthalate solvent (Figure 15). It means either that the P M M A transition temperature range in the dibutyl phthalate solvent exists above the temperature range studied (which seems to be supported by the presence of two types of spin-label in the sample at 333 K) or that no conformational transition of PMMA in this solvent occurs at all. It should be mentioned that the described break can hardly be observed when the spin-label rotational dynamics is characterized by the rotational diffusion parameter R = (R,Rll,)]lz or by the correlation time rR = (6R)-], because the activation energies of R , and RIIchange in an opposite direction in the transition temperature range, and these changes may compensate each other. Breaks were not found in the plots of the data determined in the analysis of PMMA I1 ESR spectra in both solvents (Figures 16 and 17), probably because the conformational transition of the P M M A chain does not affect the rotational dynamics of the spin-label bound at the end of the polymer chain sufficiently.
Conclusions All the characteristic features of the experimental slow motional ESR spectra of both types of spin-labeled PMMA in both solvents were successfully simulated by using a corrected version of the Polnaszek‘s simulation program. It makes it possible to perform complete analysis of these spectra which consists in the determination of the three parameters R , , R , , ,and 8, characterizing the axially symmetric rotational diffusion of the spin-label. Only the broad limits of the values of parameters R , and R,,may be determined in the analysis of motional narrowing ESR spectra provided that the orientation of the spin-label rotational diffusion symmetry axis is temperature independent. With respect to the practical equivalence of the orientation of the rotational diffusion symmetry axis determined in the analysis of the experimental slow motional ESR spectra of PMMA I and the orientation of the axis of the chemical bond responsible for the spin-label internal rotation relatively to the P M M A chain segment, estimated on the basis of spin-label geometry, the component R , of the rotational diffusion tensor may be identified as the parameter Rs, characterizing the isotropic rotational diffusion of the PMMA chain segment. Analysis of the temperature dependence of this parameter revealed that the activation energies of the PMMA chain segment rotational diffusion in both solvents were much higher than the activation energies of the viscous flow of these solvents and that they differed considerably one from another. Hence, these activation energies represent the barrier for local P M M A chain motions and are solvent dependent. A sudden decrease in the activation energy found in the ethyl acetate solvent at temperatures above approximately 303 K is probably due to the conformational transition of the PMMA chain observed in a number of solvents at similar temperatures and is characterized by the sudden increase in the flexibility of the PMMA chain above the transition temperature.
