T1 Minimum Research Articles

Segmental motion in polyoxymethylene

AbstractThe proton spin‐lattice relaxation times (T1) of melt‐crystallized, solution‐crystallized, and solid‐state‐polymerized polyoxymethylene (POM) were measured between −60 and +150°C. The three types of samples each have a pronounced T1 minimum near room temperature which is a high‐frequency manifestation of the γ process. From the quantitative dependence of the relaxation intensity on crystallinity as well as from the absolute magnitude of the relaxation times, it is concluded that the γ process in POM arises from hindered rotation of noncrystalline chain segments. The relation between the relaxation times and the long period indicates that these noncrystalline segments constitute disordered lamellar surface layers, the thickness of which depends on thermal history of the material. The temperature dependence of the motion of the relatively thin surface layers of solution crystallized POM is quite straightforward. The γ process in the bulk‐crystallized material involves cooperative motion, however, leading to temperature‐dependent kinetic parameters.

NUCLEAR RELAXATION, SPIN ECHO AND PARALLEL PUMPING IN Y3Fe5O12

The influence of parallel pumping on NMR echo signal in Y3Fe5O12 have been studied. Possible mechanism of transverse nuclear relaxation caused by the damping and scattering of parametric spin waves is considered. The spin lattice relaxation in polycrystalline sample have been investigated in the 4.2-400 °K temperature interval. The minimum of T1 which it was supposed due to Fe2+-Fe3+ valence exchange was found at 300 °K.

Nuclear spin relaxation and self-diffusion in the binary system, dimethylsulphoxide (DMSO)+ water

Spin-lattice (T1) and, where appropriate, tranverse (T2) relaxation times are reported for the protons in DMSO + water mixtures over a range of temperature and composition. Self-diffusion coefficients are also measured. A minimum in T1 for a d6-DMSO + H2O sample enables rotational correlation times for water molecules to be evaluated in mixtures with mol fractions of water, x(H2O), ⩽0.7. The low temperature (170-250 K) behaviour of T1 for DMSO + D2O mixtures with x(D2O)≃0.7 is interpreted in terms of end-over-end rotation of DMSO molecules and internal rotation of methyl groups. Under certain assumptions rotational correlation times for the DMSO molecules are obtained from the intramolecular contribution to T1 derived from measurements on ternary mixtures of the type d6-DMSO + DMSO + D2O. These are found to be very similar to those for the water molecules at the same temperature and compositions suggesting that the DMSO and water molecules reorient together. All measurements indicate a minimum in molecular mobility, both rotational and translational, at around a mol fraction of water of 0.65.

Determination of spin–rotation interaction constants in fluorinated methane molecules by means of nuclear spin relaxation measurements

The proton and fluorine spin relaxation time T1 has been measured in CH4, CF4, CHF3, and CH3F gases at low densities. By measuring the dependence of T1 on density near the characteristic T1 minimum, new information has been obtained on the spin–rotation interaction coupling constants in CF4, CHF3, and CH3F. The CH4 system was used to test the validity of this method since the spin–rotation coupling constants are accurately known for CH4. The correlation function for the spin–rotation interaction was found to be exponential within experimental error for all of the molecules studied. In the analysis of the experimental data, the effects of the dipolar interactions and of nuclear spin symmetry considerations were completely neglected. The validity of these approximations is discussed in the Appendix.

Nuclear relaxation in atactic polystyrenes: T1 and T1ρ measurements

AbstractMeasurements have been made on a series of linear atactic polystyrenes whose molecular weights range from 900 to 1.8 × 106, where Mw/Mn ≪ 1.2. Spin lattice relaxation times have been measured in the laboratory frame (T1) and in the rotating frame (T1ρ) in the temperature range 90–500°K. Two major relaxation minima were observed in both sets of measurements. The high temperature process corresponds to the glass transition (α process), the position of the minimum depending on the chain length. The low temperature process appears to originate from the n‐butyl endgroups in the polymer, its position being independent of chain length while its intensity is inversely proportional to molecular weight. No other minima were observed, in contrast to some other observations made by broadline and pulsed NMR techniques. Relaxation was exponential in all cases except in the region of the high temperature T1ρ minimum and above. This nonexponential behavior is possibly connected with the transition at T > Tg observed by a number of other techniques and which is thought to correspond to a transition between two types of liquid state. A correlation frequency diagram has been drawn for all the processes observed in polystyrene by other techniques, (α, β, αβ, γ, and δ) which shows that the T1 and T1ρ minimum positions correlate well with the α process and that there is a possible contribution to the relaxation due to the γ process on the low temperature side of the α process. At these measurement frequencies the α and β processes are merged into an αβ process. There is no evidence for a contribution from the mechanical δ process. The effect of the endgroups is observed to very high molecular weights (4.98 × 105), and it seems that a three‐dimensional diffusion model would be more adequate than the one‐dimensional model used to interpret similar behavior of paraffins and polyethylenes. Measurements of T1 in the low‐temperature region would constitute a method for a rough measurement of the molecular weight of these polymers.

Spin lattice relaxation in linear polyethylene

AbstractThe proton spin‐lattice relaxation times (T1) of linear polyethylenes (PE) of varying morphology were measured as a function of temperature. The T1 of oriented bulkcrystallized and solution‐crystallized material was isotropic, in disagreement with calculations based on a sample dipole pair model. Motion in the non‐crystalline regions of the samples is shown to be responsible for the T1 minimum occurring around −20°C. The dependence of T1 at the minimum on the long period reinforces the model of an amorphous fraction composed of disordered lamellar surface layers. The temperature of the T1 minimum and the dependence of T1 on the long period imply that the mobility of these amorphous regions is reduced in cold‐drawn and solution‐crystallized samples. This mobility irreversibly increases with annealing. In highly relaxed samples the motion of a small portion of the disordered regions is almost liquidlike, as indicated by the presence of a second shorter T1.

Nuclear spin-lattice relaxation by two-fold correlated spin reorientation

A calculation by Look and Lowe of the dipolar relaxation in a spin system where each spin jumps randomly between two equilibrium positions is extended to include correlated motion. A two-proton system is used as an example and the predicted variation of the minimum of T1 with the angle between the interproton vector positions is shown graphically for various interproton distances. The extension to a multi-spin system is indicated and the procedure for calculating T1 in polycrystalline material is discussed.

Effect of CH3-reorientation on spin-lattice relaxation time in ketones

The influence of CH3-reorientation on the spin-lattice relaxation time T1 in 6 solid ketones has been investigated. The results of the T1 measurements can be explained by assuming that a sufficiently rapid reorientation of a methyl group takes place only when this group is separated from the keto group by at least one methylene group. At about –100°C, a T1 minimum is observed which is a measure of the ratio between the total number of protons and the number of reorienting methyl protons. Deuteration of the methyl group adjacent to the keto group gave for [1,1,1,3,3-2H5]-2- pentanone a T1 minimum which is within 10% of that expected on the ground of the above-mentioned assumption. The T1 minimum for [1,1,1,3,3-2H5]-2-butanone deviated 30 %, which is probably due to contaminations and the absence of methyl-methylene interactions. The activation energy of the CH3-reorientation appears to increase according as the reorienting methyl group approaches the CH3CO group. It varies from 2.8 ± 0.2 kcal/mole for 2-tridecanone to 3.5 ± 0.2 kcal/mole for 2-pentanone. The asymmetry in the T1-curves can be explained by assuming an asymmetric correlation time distribution, which causes a variation of 3 % at most in the T1 minimum.

Ion Motion in Tetrafluoroborate Salts. I. NH4BF4 and ND4BF4

Proton and fluorine NMR data in NH4BF4 and its totally deuterated analog reflect the presence of isotropic and rapid BF4− tumbling as well as onset of isotropic NH4+ ion motion in the orthorhombic phase. A linewidth transition in the 19F spin system from 19±1 G2 at 133°K to 2.5±0.5 G2 at 198°K and 19F thermal relaxation times measured in ND4BF4 from 210° to 478°K yield a span of 19F correlation times from 3×10−4 sec (168°K) to 6.4×10−11 sec (472°K). The transition to the cubic modification at 472°K decreases the 19F correlation time to 2.6×10−12 sec (478°K). Above 318°K, fluorine relaxation in NH4BF4 is dominated by intraionic dipolar interactions, while below this temperature cross relaxation with protons located on neighboring ammonium ions becomes evident. Deuteration removes this contributor to the 19F relaxation. The apparent activation energy for BF4− motion is slightly dependent upon temperature, and increases somewhat with increasing temperature. The pre-exponential factor associated with 19F correlation times above 318°K is abnormally small, possibly reflecting a decrease in the effective moment of inertia by mechanical coupling between BF4− motion and NH4+ motion. Crystallographic measurement of the orthorhombic unit cell parameters from 190° to 296°K shows rapid linear expansion of a and c axes in the range 190° to 260°K, with a marked decrease in the rate of variation of these axis lengths with temperature above 260°K. In the same temperature region a shallow proton T1 minimum is observed, which may be associated with the modification of NH4+ ion motion by lattice expansion or simply due to cross relaxation with the 19F spin system. Proton T1 data also show a shallow plateau at higher temperatures due to interionic dipolar coupling and the BF4− motion. The x-ray data suggest the possibility of a subtle crystallographic change at low temperatures. A small linewidth transition is observed for the proton spin system in the range 173°K (4.0±0.1 G2) to 223°K (2.9±0.1 G2) apparently associated with interionic dipolar coupling.

Nuclear Magnetic Relaxation in Magnetite

The nuclear magnetic relaxation of 57Fe on tetrahedral sites in polycrystalline magnetite has been studied by spin-echo method with special interest in the relation to the low temperature transition and the electron diffusion among octahedral sites. Spin-lattice relaxation time T1 increases from about 0.7 msec at room temperature to 9 msec at 130°K. At the transition point (118°K) T1 decreases abruptly by the factor of about seven. It makes a minimum of 0.6 msec at about 88°K, then increases with decreasing temperature up to about 500 msec at 4.2°K. The minimum of T1 may be interpreted by the electron diffusion among B sites. This effect is considered to be dominant from the transition temperature to liquid-nitrogen temperature. The discontinuity of the relaxation time at the transition temperature suggests that the hopping frequency increases very rapidly as the order collapses and this mechanism becomes no more effective to the nuclear magnetic relaxation. Spin-spin relaxation time T2 is equal to T1 above about 60°K and becomes smaller than T1 below that temperature. T2 (=10 msec) at 4.2°K may be attributed to Suhl's interaction.

Relaxation phenomena in high polymers

AbstractThe principles of the nuclear magnetic resonance, NMR, and dynamic mechanical methods and their use for the investigation of segmental motion in high polymers are briefly discussed. Mechanical loss‐temperature data have been obtained from 4.2°K. at audiofrequencies for various addition type high polymers along with NMR line‐width or second moment and NMR spin‐lattice relaxation time, T1, data from 77°K. The examples include a linear polymer, polyethylene, PE, four polymers with mono‐substituted repeat units, polypropylene, poly(4 methyl pentene‐1), poly(ethylacrylate) and polystyrene (PS), and three polymers with disubstituted repeat units, poly(methyl methitcrylate), poly(ethyl methacrylate) and poly(alpha methyl styrene). For all but PE and PS NMR line narrowing processes and T1 minima, attributed to methyl group reorientations, are found at low temperatures. Molecular motion, usually occurring above room temperature as a consequence of the glass to rubber transformation, leads to the appearance of a mechanical loss maximum, further NMR line narrowing, and a T1 minimum. Mechanical loss maxima, possibly due in some cases to side‐chain (other than methyl) reorientations and in other cases to main chain oscillations are also evident.

NMR Relaxation Times in Solid White Phosphorus: Diffusion and Rotation

Nuclear magnetic resonance relaxation times have been measured for solid white phosphorus by spin-echo techniques. The diffusion coefficient calculated from T2 in the α phase can be represented as D=D0exp(−ΔH/RT),where D0=0.077±0.014 cm2/sec, and ΔH=12.1±0.1 kcal/mole. The correlation time for rotation calculated from T1 in the β phase can be represented by tc=t0exp(ΔH/RT),where t0=6.04×10—14 sec, and ΔH=4.02±0.02 kcal/mole. The distance between phosphorus atoms in the P4 molecule is found to be 2.24±0.03 Å from the value of T1 at the T1 minimum in the β phase.

Magnetic-Resonance Studies of Lithium Vanadium Bronze

The nuclear magnetic resonance of Li7 in LixV2O5 shows no Knight shift, but there is a small diamagnetic shift relative to LiCl solution, amounting to 0.0023 and 0.0058% at 296° and 77°K, respectively. The spin—lattice relaxation time T1 as measured by pulse experiments, decreases from 0.16 sec at 296°K to a minimum of 0.060 sec at 163°K and then rises to 0.13 sec at 77°K. The free-induction decay half-width decreases from 850 μsec at 296°K to 100 μsec at 77°K. The minimum in T1 is attributed to back-and-forth motion of the lithium ions within but normal to the axis of channels in the oxygen framework; the line narrowing, to diffusion along the channel from one unit cell to an adjacent one. EPR studies give Lorentzian-shaped lines, centered at g=1.96, of intensity proportional to 1/T. Results are consistent with a model in which lithium atoms in a host V2O5 structure are completely ionized to give Li+ ions and electrons which are almost, but not completely, localized as V4+ centers.

Proton Magnetic Resonance Studies on Hexamethylenetetramine—Structure, Molecular Reorientation, and Impurity Diffusion

Nuclear magnetic resonance measurements on protons in solid hexamethylenetetramine have led to information about the molecular structure and motions and diffusion of impurity water molecules in the solid. The information obtained is consistent with previous work indicating that the solid contains distorted molecules with a C–H distance of 1.13 A in a body-centered cubic crystal structure. From temperature dependences of a linewidth transition at 375°K, and a relaxation time minimum at 550°K, a rotational activation energy of 18 kcal/mole was computed. Sublimation, with a latent heat of 18 kcal/mole, occurs at the same temperatures as the rotation. Intermolecular C–H···N hydrogen bonds are the source of both the stability of the crystal and the barrier to rotation. The energy of these bonds appears to be 1.2 kcal/mole per bond. It was determined that a water impurity was present, in an amount of about 0.1% by weight, and was diffusing in the solid. The diffusion produced an anomalous minimum in T1. Rough analysis of the T1 minimum, using the theories of Bloembergen, Purcell, and Pound and of Torrey, yielded values of the infinite temperature diffusion coefficient D0 for the water of 10—3 to 10—1 cm2/sec and an activation energy of 5 to 7 kcal/mole.