Proton spin-lattice relaxation times have been measured at 16, 31, and 59 MHz in 4-methyl-2,6ditertiarybutyl phenol between 80 K and its melting point, 340 K. The variation of T1 with temperature shows too distinct minima. The lower-temperature minimum has been analyzed in terms of relaxation by reorientation of four of the six t-butyl methyl groups with an average apparent activation energy of about 2.4 kcal mole −1 (104 meV molecule −1). The highertemperature minimum has been analyzed in terms of relaxation by reorientation of the t-butyl groups about their C3 axes with four of the six t-butyl methyl groups reorienting very rapidly, and the remaining two reorienting with correlation time similar to that of the t-butyl group. The activation energy for the higher-temperature minimum is 5.76 kcal mole −1 (250 meV molecule −1). Steric potential calculations are used to add weight to these assignments, and a number of peculiarities displayed by the lower-temperature minimum are discussed.

Broad-line n.m.r. investigations of a series of complexes of boron trifluoride with amine donor molecules (e.g., BF3 . NH3) reveal the presence of molecular motion in the solid state. From the temperature dependence of the linewidths, activation energies are derived for the reorientation process. The observed values of the second moments of the absorption signals are compared with theoretical values calculated from the known X-ray structures assuming motion of different parts of the complexes. The motions are discussed in relation to the crystal and molecular structures of the various complexes.

The proton magnetic resonance absorption in anhydrous sodium stearate has been investigated over the temperature range -182OC t o 200' C. An abrupt change in the line width and the second moment has been observed between 113" C and 114" C, which corresponds to a known phase transition. The results suggest that a t temperatures below 114" C the motion of the hydrocarbon-chain portion of the sodium stearate molecule is chiefly one of oscillation or rotation about the chain longitudinal axis. The hydrocarbon chains may be free t o move about other axes a t temperatures above 114" C, although the molecule as a whole retains a fixed position in the crystal lattice. INTRODUCTIONThe various mesomorphic phase transitions in sodium salts of long-chain fatty acids have been exteilsively studied by several physical methods (1). X-Ray, infrared, and nuclear nlag~letic resonance studies have indicated that the lower temperature transitions may represent the onset of rapid reorientation in the paraffin-chain part of the sodium soap lllolecule (2, 3, 4). Of particular interest are the phase transitions curd-supercurd a t 89-92" C, supercurd-subwaxy a t 110-117" C, and subwaxy-waxy a t 125-135" C (4). The followil~g is a proton magnetic resonance investigation of these transitions in sodium stearate, and is an extension and correction of the work in a previous communication (4). E X P E R I M E N T A LThe sodium stearate was prepared from Eastman Kodalc white label stearic acid, f.p. 68.1" C, which had been purified by repeated crystallization a t -20" in acetone (5). The purified acid, f.p. 69.2" C, was dissolved in hot ethanol and titrated t o a phenolphthalein end point with an aqueous ethanol solution of sodium hydroxide. The sodium stearate precipitate was filtered, dried in air, and melted under vacuum t o remove residual solve~lts and t o render it anhydrous (6). This compact, fused soap was remelted under vacuum in sample tubes; dry nitrogen was admitted t o the system and the tubes were sealed off.The nuclear magnetic resonance spectrometer and the nlethods of temperature coiltrol have been described previously (7). The temperature of the sample was measured with a ther~nocouple inserted in a well in the side of the sample tube. T h e line width was talcen as the separation in gauss between points of maximum and rninimunl slope. The second moments of the resonance lines were obtained from the experimental derivative curves (8) by numerical integration and were corrected for the effects of modulatio~l (9). RESULTSThe proton magnetic resonance line widths, measured from -68" C t o 130" C, are given by the open circles in Fig. 1. The line width was also measured a t -182" C where it is lG.l gauss. Particularly notable is the extensive decrease in the line width a t temperatures above 30" C, and the abrupt change from a width of 2.8 gauss a t 113" C to a width determined by the field homogeneity a t 114" C. This abrupt narrowing coi~lcides with 'Manuscript

Kuclear magnetic resonance spectra and the infrared absorption between 700 and 760 cm-I have been observed a t temperatures near the melting points of the even-numbered fatty acids from Cl8 to Clo. The results are interpreted as indicating breakdown of crystalline character and onset of liquid-like motion a t scattered points in the solid structure several degrees below the melting point, and increasing in extent as the melting point is approached.A proton magnetic resonance study of anhydrous stearic acid (I) gave some quantitative indication of liquid-like molecular motion occurring in part of an otherwise rigid lattice a t temperatures several degrees below the melting point. I t seemed appropriate to look for this behavior, which was considered to be a premelting phenomenon (2), in other fatty acids and by other methods. Acids with an even number of carbon atoms from palmitic (C16) to capric (Clo) have been examined by nuclear magnetic resonance, and the change with temperature of the shape of the infrared absorption band a t about 720 cm-I has been studied for the even-numbered acids from stearic (C18) to lauric (Clz).This infrared band, which is characteristic of hydrocarbon chains (CHZ), with n >, 4, is frequently a doublet below the melting points of the compounds showing it, and a singlet above the melting point or for the compound in solution. I t has been assigned to the CH2 rocking mode (3, 4). A series of higher normal modes of CH2 rocking has been identified in the spectra of n-paraffins in the range 720-1050 cm-I (4). These bands are of much lower intensity than the first mode a t 720 cm-l, and their number depends on the length of the methylene chain. Stein has used the strong absorption of the first mode in a n investigation of the crystallinity of polyethylene (5), attributing the component of the doublet a t 720 cm-I equally to crystalline and amorphous parts of the polymer and the component a t 730 cm-I exclusively to crystalline parts. The splitting of the band was explained by the perturbation of the CH2 rocking vibration by the interaction of nearestneighbor methylene chains in the crystalline array. I t was shown (6) that the crystal field shifted the frequency of the out-of-phase rocking mode only slightly to higher energy and that the frequency of the in-phase mode was moved much further to higher energy. In an amorphous substance (solid, liquid, or solution) the unperturbed band occurs a t essentially the same frequency as the out-of-phase mode in the crystalline substance. Changes with temperature in the intensity of this band have also been used to study phase transitions in waxes (7). In the work reported here, the variation with temperature of the integrated intensity of the components of the doublet has been examined as a possible indication of loss of crystalline character in fatty acids below the melting point.The acids used in this investigation were all Eastman Kodak white label grade that were further purified by repeated recrystallizations from acetone following the...

The mechanical behavior of an idealized linear polymer is discussed in terms of the Maxwell relaxation theory. When a simple rectangular distribution of relaxation times is assumed, it is shown that the dynamic properties can be related to those deduced from stress relaxation data by the equation: where ηdyn is the dynamically measured internal friction or viscosity, ω the radian frequency, and E° the negative slope of the relaxation curve plotted as reduced stress vs. log 10 time. Application of this equation to values of ωη dyn and stress relaxation data on rubbers obtained by Dillon, Prettyman, and Hall [5] and data on textile fibers by Dunell and Dillon [6] is made. Better than order-of-magnitude agreement was obtained between dynamically measured values of ωη dyn and those calculated by the above equation for the series of rubber stocks and fibers considered. The theory presented has interesting implications in regard to the structures of the various polymers studied, most of which would not a priori be considered linear in the sense of the idealized model. The relationships deduced from the "box" distribution are extended to other broad distributions of relaxation times. Stress Relaxation and General Elastoviscous BehaviorThe simplest type of elastoviscous behavior was postulated by Maxwell to obey the equation where s is a component of strain (e.g., simple tensile strain), f is a component of stress (e.g., tensile stress), E is the elastic modulus, and T is the socalled relaxation time of the system. A mechanical model which behaves in the manner defined by equation (1) is a spring and dashpot connected in series, if the elastic constant of the spring is taken as E and the damping constant or viscosity of the dashpot is taken as TE. This mechanical system is known as the Maxwell model. If a substance which obeys equation (1) is rapidly extended to a fixed strain so and maintained at that strain, the stress will decay according to the law Certain substances exist whose relaxation behavior approximates equation (2)-e.g., Hevea gum vulcanizate [16~ and polysulfide rubbers [12~ at high temperatures, where the elastoviscous behavior is controlled by chemical reactions. In relaxation curves obeying this equation, the decay of stress occurs almost completely within two cycles of logarithmic time. When this relaxation function is plotted against logarithmic time as abscissa, a change in the value of the relaxation time, T, merely shifts the relaxation curve horizontally along the logarithmic time axis.The decay of stress in polyisobutylenes maintained at constant extension and temperature does * This article is based on a thesis submitted by Basil A.Dunell in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Princeton University.

Broad-line nuclear magnetic resonance (n.m.r.1 and spin lattice relaxation time measurements on solid coronene indicate the presence of a molecular reorientation process at 160 OK. The activation energy for the process has been determined at 5.9 kcal/mol and the nature of the motion deduced as being reorientation in the plane of the molecule. No motional processes are observed for perylene or triphenylene.The results are discussed with respect to thermodynamic data and the molecular structures.La largeur de raie en r.m.n. ainsi que les mesures du temps de relaxation spin reseau de coronene solide indique la presence d'un processus de reorientation a 160 OK. L'Cnergie d'activation du processus a Cte determinee comme etant de 5.9 kcal/mol et la nature du mouvement a kt6 prkcisee comme Ctant une orientation dans le plan de la molecule. Aucun processus de mouvement n'a kt6 observe pour le perylene et tryhtnylene. Les resultats sont discutts en fonction des donntes thermodynamiques et des structures moleculaires.

Spin-lattice relaxation times, T I , have been measured over appropriate temperature ranges for sulphamic acid (NH3S03), caesium trifluoromethanesulphonate (CF3S03Cs) and caesium methanesulphonate (CH3S03Cs). Reorientation about the C3, axis of the three-spin proton or fluorine system in each substance accounts for the observed relaxation rates. Activation energies have been obtained for all the reorientations and in the cases of sulphamic acid and caesium methanesulphonate, whose crystal structures are known, related to the hydrogen bonding in NH3S03 and to the C--He * -0 and C--Ha * .H interactions in the caesium salt. Even though a 3-fold rotor in sulphamic acid reorients in a very roughly 5-fold environment, the external barrier is not especially small due to a departure from perfect 5-fold symmetry in the environment. Failure to obtain close agreement between barrier height and activation energy should probably be attributed to an oversimplification in the assumptions about the form of the barrier potential. Singularly good agreement is obtained between the n.m.r. activation energy (17.5 kJ mol-') for the caesium salt and the rotational barrier derived from inelastic neutron scattering results. The activation energy for the reorientation of the CF3 group in CF3S03Cs is markedly dependent on temperature in a manner which is overall non-linear.

Broad-line and pulsed proton magnetic resonance spectra of trimethylamine-trimethylborane have been obtained in the temperature range from approximately liquid-nitrogen temperature to 350 K. Motions of and within the molecules are deduced from a comparison of the observed second moments at various temperatures with theoretically estimated second moments. Reorientation of the methyl groups attached to boron, at frequencies sufficient to narrow the n.m.r. line, is observed at the lowest temperature attained, whereas reorientation of the methyl groups attached to nitrogen and reorientation of the whole molecule at n.m.r. line width frequencies occur simultaneously at higher temperatures. Two minima in the curve of spin-lattice relaxation time as a function of frequency can be interpreted in terms of these reorientational motions, and activation energies are calculated for the reorientation processes.