Electron Spin Resonance Studies of Spin-Labeled Polymers dergo ring opening in neutral and alkaline solutions, although previous optical pulse radiolysis results* suggested that the OH adduct to pyrrole undergoes a ring opening in acid solution. On the other hand, elimination of a water molecule (the OH added and the H from NH) takes place with some OH adducts of pyrroles and imidazoles. This elimination is more rapid in pyrroles than in imidazoles, is more rapid in the unsubstituted compounds as compared to the carboxy derivatives, and is catalyzed by base. In fact, water elimination from any of the carboxy derivatives examined was not detected at all, whereas with pyrrole the initial OH adduct was not observed. All the OH adducts undergo a rapid exchange of the OH proton, at pH >10 for imidazoles and >11 for pyrroles, resulting in a loss of the OH proton splitting with no change in the other hyperfine constants. The OH group of the adducts dissociates with pK = 12 for the case of 4,5imidazoledicarboxylic acid and pK = 13.5 for 2-pyrrole-
1635
carboxylic acid and its N-methyl derivative. This dissociation results in changes in all the hyperfine constants, and in the intermediate region weighted average hyperfine constants have been observed, with no apparent change in line width. This fact indicates a rapid exchange between the acid and basic forms.15 The addition of OH to isoxazole was found to take place on the carbon adjacent to the oxygen rather than that adjacent to the nitrogen. The OH adduct is expected to undergo ring opening in alkaline solutions as in the similar case of furans, but this process could not be detected because of basic hydrolysis of isoxazole itself. Addition of OH to pyrazole occurs a t the 5 position next to the NH group and results in an allylic type radical. When the 5 position is sterically hindered by a carboxyl group as in the case of 3,5-pyrazoledicarboxylicacid, addition was found to take place preferentially at the 4 position.
Electron Spin Resonance Studies of Spin-Labeled Polymers. II 1. The Molecular Weight Dependence of Segmental Rotational Correlatiori Times of Polystyrene in Dilute Solution A. T. Bullock,” G. G. Cameron, and P. M. Smith Department of Chemistry, University of Aberdeen, Old Aberdeen, AB9 ZUE, Scotland
(Received December 73, 19721
Seven narrow fraction polystyrenes have been spin labeled with nitroxide radicals and electron spin resonance spectra of dilute solutions of the polymers in toluene have been recorded over a range of temperatures. Line width analysis yields values of the rotational correlation time. A local mode of segmental reorientation has been characterized a t high molecular weights and has an activation energy of 4.3 kcal mol-1. Rotation of the whole molecule makes a significant contribution to the relaxation process at low molecular weights. The activation energy for this rotational mode agrees well with that for viscous flow of the solvent, namely, 2.15 kcal mol-I.
Introduction The technique of spin labeling is now reasonably well established. Briefly, a stable free radical is covalently bonded to a macromolecule and the electron spin resonance (esr) spectrum of the labeled polymer is examined. In solution, which is our concern here, measurement of the widths of the esr lines can give information about the dynamics of the polymer chain. The class of free radicals most widely used for labeling to date is the nitroxide group.1 Members of this class have the necessary properties of high stability and well-defined anisotropic g tensors and hyperfine coupling tensors to the I4N nucleus. Most of the published work in this field re-. lates to biopolymers2 but recently Lindberg and coworkers3,* together with the present authors536 have demonstrated that spin labeling provides a useful additional
technique to the established methods of nmr spin-lattice relaxation, dielectric dispersion, viscoelastic relaxation, and fluorescence depolarization in the study of the dynamics of synthetic macromolecules in solution. In part I of this series5 we described the preparation of a “lightly labeled” polystyrene which had a wide distribu(1) J. D. Ingham, J. Macromol. Sci., Rev. Macromol. Chem., 2, 279 (1968). (2) 0. H. Griffith and A. S. Waggoner, Accounts Chem. Res., 2, 17 (1969). (3) p. Tbrmaia, K. Silvennolnen, and J. J. Lindberg, Acta Chem. Scand., 25,2659 (1971). (4) P. Tormala, J. J. Lindberg, and L. Koivu, Pap. Puu, A Painos, 4, 1 (1972). (5) A. T. Bullock, J. H. Butterworth, and, G. G. Cameron,‘Eur. Polym. J., 7, 445 (1971). (6) A. T. Bullock, G. G. Cameron, and P. Smith, Polymer, 13, 89 (1972). The Journalof PhyslcalChemistry, Vol. 77, No. 13, 19TB
1636
A. T. Bullock, G. G.
Cameron, and
P. M. Smith
tion of molecular weights centered on ca. 115,000. Comparison of the results with those obtained by other techniques, notably dielectric dispersion in poly@-chlorostyrene),7xs suggested that a segmental or "local mode" of rotational diffusion of the polymer was observed. The present study is concerned with a careful delineation of the dependence upon molecular weight of the correlation time for diffusive rotation of the nitroxide label and hence of that part of the macromolecule to which the label is attached. Experimental Section Seven narrow fraction polystyrenes were obtained from Waters Associates. The number average molecular weights were 2025, 3550, 10,000, 19,700, 50,000, 97,200, and 196,000. The method of labeling and characterization of the resultant polymer has been described in part II.6,9 The labeled monomer unit has the structure shown in I.
Figure 1. Esr
spectrum of spin-labeled polystyrene (Mn = 2025)
in toluene solution ( 1 % ) ,at room temperature.
N\o t-Bu
I The labeled polymers were finally purified by two precipitations from toluene solution by the addition of methanol. Gel permeation chromatograms were run on the unlabeled, iodinated and labeled polymer to ensure that neither cross linking nor degradation had occurred. To avoid contributions to line widths from spin exchange, labeling was carried out in such a way that no sample contained more than one nitroxide radical per 160 monomer units. Usually the ratio was much smaller than this. Solutions (1% by weight) of the labeled fractions in toluene were crepared and degassed by repeated freeze-pump-thaw sequences. Esr spectra were recorded for each fraction at intervals in the temperature range 278-363 K using a Decca X3 spectrometer. Field measurements were made with a Systron-Donner 3193 digital Gaussmeter. The uncertainty in an individual field measurement is &0.01 G (0.03 MHz) but field differences can be obtained to a slightly greater precision by careful interpolation. Spectral simulations and least-squares analyses were performed on an I.C.L. system 4/50 computer. Theory and Method of Line Width Analysis The spectrum of the labeled polymer in solution is shown in Figure 1. Clearly the electron couples not only with the 14N nucleus but also with the aromatic protons. These will have anisotropic hyperfine tensors and the rotational motion of the radical will modulate the coupling between the electron, the protons, and the 14N nucleus. This, combined with the effect of an anisotropic g tensor, gives rise to line widths which depend on the various nuclear quantum numbers mt and which are expressed by the equationlo Tz-'(ml,m2...,m,) = A
+ e B , m , + kCim,z + i=l
i=l
2 Ei,mimj
(1)
,#,=I
The coefficients A , B, C, and E are defined in the literature.10 At present it is only necessary to note that they are The Journal of Physical Chemistry, Vol. 77, No. 13, 7973
functions of the applied magnetic field, certain spectral densities, and various inner products of the g and hyperfine tensors. Fortunately in the present case it is possible to select lines for which Z m H , the resultant proton spin quantum number; is zero. The line width expression then depends only on mr. the component of the I4N nuclear spin, the g anisotropy, and the anisotropy of the coupling tensor to 14N. Explicitlyll
where A Y = -(lPlh)[gz - '/Z(gx + gJ1, b = (4a/3)[A Y'(B C)], and u = l / ( l ~ 0 % ~ ~ The ) . symbols have the following meanings: A, B, and C represent the z, x, and y components of the hyperfine tensor in Hz; WO, represents the Larmor angular frequency of the electron; Bo, the applied magnetic field; T ~ the , rotational correlation time, and X,the broadening by other mechanisms independent of mI. The parameter u represents nonsecular contributions to the line widths. As T~ in all cases in this work was greater than ea. sec, u was negligible a t the microwave frequency employed ( W O = 27r x 9.27 x 109 rads sec-1). Omitting nonsecular contributions, eq 2 becomes
+
+
1
4 -bAyBomI rC X (3) 15 A more convenient form of this has been proposed by Stone, et a1.12
+
(7) W. H. Stockmayer, Pure Appl. Chem., 1 5 , 539 (1967). (8) B. Baysal, B. A. Lowry, H. Yu, and W . H. Stockmayer, "Dielectric Properties of Polymers," F. E. Karasz. Ed., Plenum Press, New York, N. Y., 1971, p343. (9) Minor modifications of the labeling technique have been made recently. Details are available on request. (10) A. Hudson and G. R. Luckhurst, Chem. Rev., 69,191 (1969). (11) G. Poggi and C. S. Johnson, Jr., J. Magn. Resonance, 3, 436 (1970). ( 1 2 ) T. J. Stone, T. Buckman, P. L. Nordio, and H. M. McConneli, Proc. Nat. Acad. Sci. U. S., 54, 1010 (1965).
Electron Spin Resonance Studies of Spin-Labeled Polymers
1637
Recorded (a) and simulated ( b ) spectra of the central multiplet ( m =~ 0); see text.
Figure 2.
Figure 3.
width.
Calibration
plot of
observed vs. true peak-to-peak line
1.7 , h
-0
9 1.6-
5 1.5 8 v
9- 1.4h
-TI? 1.3-
9 1.2 h
U
-
1.1 1.o
i
I
1.I
1.2
i
i
1.3 1.4 T2(o)/G(t1)(true)
I
1.5
1.6
Calibration plots of observed [ Y ( 0 ) / Y ( & 1 ) ] 1 / 2 vs. T 2 ( 0 ) / T 2 ( f l ) for the following values of Av(=[1.732aTz(O)]-’) in (a) 1.90, (b) 2.00, (6) 2.10, (d) 2.20, (e) 2.30,and (f) 2.40.
Figure 4.
1
8 7, b2T z (O)m: ( 4 ) Defining the ratios Tz(O)/Tz(+l), T2(0)/T2(-1) as R+ and R - , respectively, it is readily shown that
+
R, R- - 2 = (1/4)~,b~Tz(O) (5) Sensitive measures of R+ and R - are obtained from the ratios of peak-to-peak intensities, Y,of the relevant lines, thus R,
=
[Y(O)/Y(fl)]‘i2
(6)
The parameter b was obtained by measuring the separation between extremes in the powder spectrum of the solid labeled polymer and combining this measurement with the isotropic solution value of U N as described in part 1.5 Tz(0)and R , are measured from the experimental spectra but both must be corrected for the inhomogeneous broadening which results from the unresolved coupling to the tert-butyl protons.11 An experimental spectrum was chosen arbitrarily and the center multiplet (mI = 0) was synthesized with various values of the ring proton couplings, the tert-butyl pro-
MHz:
ton couplings, and Tz(O),the line width parameter of the input Lorentzian line. Figure 2 shows a comparison between the recorded central multiplet and a simulated spectrum. The values of the hyperfine coupling constants finally selected were a H ( 2 , 6 ) = 2.48 MHz, U H ( 3 , 5 ) = 5.56 MHz, and u t - B u = 0.21 MHz. Previously a N had been found to be 35.4 M H Z . More ~ recent and extensive measurements give the revised value of 35.0 0.1 MHz. A series of simulated spectra were then produced using the above coupling parameters and a range of values of Tz. Calibration plots of observed line widths us. true, or input, widths13 and observed (peak-to-peak ratios)lI2 us. true line width ratios were obtained and are shown in Figures 3 and 4. True values of R , and Tz(0) could thus be obtained from experimental intensity ratios and center line widths, respectively.
*
Results and Discussion Figure 5 shows the dependence of the rotational correlation time upon molecular weight a t three temperatures. At high molecular weights T~ is independent of chain length and it seems that a “local mode” or segmental relaxation process is being observed. This will be character(13) The input widths were the peak-to-peak widths AU (Hz) and are related to r, by T 2 - l = 1.732~Au. The Journalof Physical Chemistry, Vol. 77, No. 13, 1973
1638
A.
6.0
100 150 10-3nn
L
1.o
200
I
Dependence of the rotational correlation time T~ upon molecular weight at (a) 294.2, (b) 312.6, and (c) 345.2 K.
0.70 t-"
0
0 c1,
0.60
0.501
3.00
1
1
3.10
3.20
I
3.30
1
3.40
103/r, K-' Figure 6. rene with ref 14.
Composite Arrhenius plot for heterodisperse polystylabels I and 1 1 : 0, label 1; 0 , label 1 1 ; 0 , nmr from
ized by a correlation time 71m. As the molecular weight decreases the rotational frequency of the whole macromolecule increases sharply and ultimately the magnitude of the correlation time T~~~ describing this "end-over-end" rotation becomes comparable to ~1~ and contributes significantly to the relaxation process. Before making a definite assignment of the relaxation process a t high molecular weight to a segmental relaxation invohing rotation about the main chain carbon-carbon bonds it is important to eliminate two other possibilities. These are rotation about the C(4I-N and C(I,-main chain bonds. In part I5 of this series we described results obtained from a spin-labeled heterodisperse sample of polystyrene having an average molecular weight of ca. 115,000. The labeled unit in this case had the structure shown by 11. The same heterodisperse polymer was labeled
11
to give structure I and the correlation times of each sample were measured over a range of temperatures..Figure 6 shows the composite Arrhenius plot which includes a point calculated from some proton spin-lattice relaxation measurements made by McCall and Bovey.14 While the The Journal of Physical Chemistry, Vol. 77, No. 13, 1973
,
,
10 30 50
Figure 5.
0.80
T. Bullock, G. G. Cameron, and P. M. Smith
I
100
I
IO-^^"
200
/-I
860
Figure 7. (a) T~ from the TI measurements of ref 15; ( b ) spinlabeling results (this work). Both sets of results are at 317.2 K. The error bars in a contain the correlation times for all of the carbon atoms in polystyrene. The ordering of the correlation times at a given molecular weight is random.
close agreement between the correlation times for the sterically dissimilar spin labels I and I1 is not perhaps conclusive it strongly suggests that there is no significant contribution to the line widths arising from rotation about either the C(4,-N or the C[l)-main chain bonds. The activation energy for the reorientational process found from the composite data of Figure 6 is 4.7 kcal mol-1 (19.5 kJ mol- 1). Further support for this assignment of the chain-lengthindependent relaxation process was published by Allerhand and Hailstone15 during the course of the present work. These authors made 7'1 measurements on naturally abundant 13C in all positions in polystyrene using partially relaxed Fourier transform techniques. Again, a series of narrow fraction polystyrenes was used. Earlier, Allerhand, et a1.,I6 had demonstrated that 13C spin-lattice relaxation was dominated by the rotationally modulated dipolar coupling between the nucleus and the proton or protons bonded to it. For the case where ( W C + W H )
