1846
Macromolecules 1985, 18, 1846-1850
Local Motions between Unequivalent Conformations in Solid Poly(cyclohexy1 methacrylate): A Variable-Temperature Magic-Angle Carbon- 13 Nuclear Magnetic Resonance Study Franpoise Lauprgtre* Laboratoire de Physico-Chimie Structurale et MacromolBculaire associe au CNRS, 75231 Paris Cedex 05, France Joseph Virlet DEpartement de Physico-Chimie, CEN Saclay, 91191 Gif-sur- Yvette Cedex, France Jean-Pierre Bayle Laboratoire de Chimie Structurale Organique, UniversitB de Paris XI, 91405 Orsay, France. Received October 24, 1984 ABSTRACT: Variable-temperaturehigh-resolution solid-state I3C NMR experiments have pointed out the existence of side-ringmotions with correlationtimes of the order of lo4 s in solid poly(cyclohexy1methacrylate). The line broadening resulting from motional modulation of the carbon-proton dipolar coupling has been analyzed in terms of a chair-chair inversion of the side-ringbetween unequivalent conformations. Characteristics of this motion as a function of temperature have been determined. Results thus obtained are in good agreement with conclusions derived by Heijboer from mechanical measurements on the same polymer and use of conformational energy calculations. Cross-polarization (CP) magic-angle spinning (MAS) dipolar decoupled (DD) 13C NMR has proved to be a powerful tool for demonstrating the existence of molecular motions in the solid state. In a previous study,' roomtemperature spectra together with measurements of carbon-13 spin-lattice relaxation times in the rotating frame pointed out the presence of rapid ring motions, with correlation times of the order of IO4 s, in poly(cyclohexy1 methacrylate). However, in order to carry out a more precise characterization of these ring processes, variabletemperature experiments are necessary. Such variabletemperature experiments are reported in the present paper.
Experimental Section Carbon-13NMR experiments were performed at 12.07 MHz with a home-built spectrometer constructed around a 12-in. Varian electromagnet and employing external 2Hfield frequency stabilization,solid-state class-A transmitters, and a double-tuned single-coil probe.2 Spectra were obtained as a function of temperature using magic-angle spinning in a hollow cylindrical rotor made of Macor and spinning speed ranging from 1.5to 2 kHz3 The inner spinner volume was approximately 0.5 cm3. All the spectra were obtained by cross polarization from the spin-locked protons followed by high-power proton decoupling. Matched spin-lock cross-polarization transfers employed a of 32 kHz. Spectra were radio-frequency (rf) field strength (HI) recorded under the condition of optimum single contact, which was found to be 1-2 ms. In all the spectra, spin temperatureinversion techniques were employed to minimize base-line noise and roll4 Flip-back5was also systematicallyused to shorten the delay time between two successive pulse sequences. A total of 2OCO-4OOO scans was needed to obtain a good signal-to-noiseratio. Poly(cyclohexy1methacrylate) (Aldrich,194-9)is commercially available. Line-Broadening Mechanisms Line-broadening mechanisms in glassy materials have been recently reviewed.6 Some of them, the static ones (bulk susceptibility of the sample, chemical shift dispersions due to packing effects, bond distortion, and conformational inequivalence), induce only a small effect. More important may be the line broadenings arising from relaxation processes such as motional modulation of the chemical shift anisotropy' and motional modulation of the
dipolar carbon-proton coupling.6 For an aliphatic carbon in a static magnetic field of 1.4 T, the broadening due to the motional modulation of the chemical shift anisotropy can be estimated to remain less than 7 H z . ~Therefore, in the case of an aliphatic carbon in a low static field and under suitable conditions of magic-angle setting and proton-decoupling irradiation the only important cause of motional broadening comes from modulation of the dipolar C-H coupling. This mechanism is maximum when the rate of molecular motion is equal to the proton-decoupling field strength in frequency units: w1H = Y H H ~ H . For slow motions, this broadening is much larger than that due to the previous static effects. Therefore the observed full line width at midheight may be written as where the residual line width ( r T 2 J 1 accounts for the various static effects. Under the conditions that proton irradiation is applied exactly on resonance, that the sample spinning rate is much smaller than wlH, and that the motion does not change the carbon-proton distance, which means that we consider only the single-bond interactions, the transverse relaxation time T,,, resulting from this mechanism and contributing an amount ( r T 2 J 1 to the line width, is8 (7'2J1
= AcHJ(w~H)
(2)
ACH is the square of the carbon-proton dipolar coupling strength. For one proton at a distance r from the carbon under interest ACH
= yH2yC2h2/r6
(3)
J(w) is the spectral density of the fluctuations of the dipolar interaction
J(w) = 1 ~ m G ( r ) e - ' dwr7 where G ( r ) is the autocorrelation function G ( T )= F(t)F*(t + 7) with F ( t ) = (1 - 3 cos2 @ t t ) ) / 2
(4) (5)
(6)
where /3 is the angle of the vector C-H r of interest with
0024-9297/ 85 122 18-1846$01.5010 0 1985 American Chemical Society
Macromolecules, Vol. 18, No. 10, 1985
Local Motions in Poly(cyclohexy1methacrylate) 1847
m
/
H
F(P) = (4~/5)'/2yz0(P,0)
(15)
one gets
\
(F(P,)F(PJ)powder = P Z ( C O S 8)/5
(16)
and (FA2)powder
(FAFB)powder
A Figure 1. Two-potential-well model for the cyclohexyl ring in-
version.
the static magnetic field direction. The simplest form of the powder average of G(7) is G(7) = W / 5 ) exp(-7/7,)
(7)
so that J(W)
K 7c 5 1 + W%,2
=
7O-l
exp[-((AE
+ H)/RT)]
=
(9)
(70ab)-'
WB,A = 70-l exp[-(H/RT)] = (Tob)-' (10) where A E = Eg -EA, b = exp(H/RT), and a is the ratio of the equilibrium populations a = p(A)/p(B) = exp(AE/RT)
Let the correlation time 7,-1
=
7,
w~,g + WB,A
(FB')powder
with x = P,(COS e). Thus, using the expression of G ( 7 ) given by formula 13 (a2 + 2ax + 1) + 2 4 1 - x ) e x p ( - ~ / ~ , ) G(7) = (18) 5(1 a)2 Terms that are independent of 7 do not induce motional line broadening. The other terms give 4a 1-x 7, J(W) = -(19) (1 a)2 10 1 027;
+
+
When the two states A and B present equal energies (AE = 0), a = 1 and J(W)
1-x 7, 10 1 + W27,2
=-
with 7c = (7,, exp(H/RT)/2. For a CH2 carbon in the particular case of 0 = 109'28', x = -ll3,and the minimum value of T2, is 6.3 X s for an irradiation frequency of 32 kHz, assuming a value of r of 1.07 A. In the general case where a is different from 1, that is, EA is different from Eg, (TZm)-lis lengthened and can be written for a CH2 group as
. . .
(21) If a is much greater than 1, 7;l may be simplified as 7,-l = 70-l exp(-H/Rn = (b70)-l (22) In the case of fast flips of the internuclear vector from position B to A (W1H27,2
