Free Induction Decay Shape Research Articles

Chain Heterogeneity in Simulated Polymer Melts: Segment Orientational Autocorrelation Function

The dynamic heterogeneity of polymer chains is characterized by the lower correlation times of its end Kuhn segments with respect to those of the middle segments. In this study, the heterogeneity was investigated using molecular dynamics simulation of freely jointed chains of various lengths in the melt. Our characterization of the segmental dynamics along the chain additionally revealed the heterogeneity of rotational anisotropy, which was also lower for chain-end segments compared to those for chain-middle ones. This heterogeneity can be quantitatively characterized by intra-segmental residual dipolar coupling, which influences the transverse magnetic relaxation rate of the various chain segments and, ultimately, defines the free induction decay shape for chains of any length. Further, in the second part of this report, the origin of this relationship is discussed in detail.

The Effect of the End Segments on the Dynamics of a Polymer Melt: The Frequency Nature of the Effect and Possibility of Experimental Observation in the Free Induction Decay of Deuterons

It is shown that, in the melts of linear macromolecules, the effects of dynamic heterogeneity associated with the presence of end segments are not vanishingly small in the limit $$N \to \infty $$, where $$N$$ is the number of Kuhn segments in the macromolecule. The effect has a frequency nature, i.e., the division of the segments into “end” ones, more mobile in comparison with the “median” ones, mainly depends on the observation time. With the increase in the observation time, symmetrical growth of the “end” regions of the polymer chain occurs from both ends of the macromolecule which covers the entire macromolecule at times on the order of the terminal relaxation time. The effect generates nontrivial experimentally observed consequences. For example, the free induction decay of deuterons in monodisperse polymer melts of macromolecules should have an extended region with the exponential decay law $$g(t) \propto {{t}^{{ - \beta }}}$$, where $$\beta = 1$$ for the reptation model and $$\beta = {{(\alpha - 2)}^{{ - 1}}}$$ for isotropic renormalized Rouse models: $$\alpha > 2$$ is the exponent of the molecular weight dependence of the terminal relaxation time of macromolecules. At $$\alpha \leqslant 2$$, the influence of the effects of dynamic heterogeneity on the shape of free induction decay is weaker, although it is observable at sufficient accuracy of the measurements.

Oscillating Free Induction Decay in Polymer Systems: Theoretical Analysis

It is shown that during the Anderson-Weiss transformation derivation, as applied to a reptating polymer chain, the spin system can be divided into two sub-systems: an ergodic fluctuating one and a nonergodic quasi-static one. Consequently, the free induction decay (FID) expression is factorized. The factor with a fluctuating dipole-dipole interaction for an arbitrary correlation time is transformed into the generalized Anderson-Weiss exponential, and the factor with a quasi-static dipole-dipole interaction in an isotropic polymer melt is transformed into the oscillating Fourier image of the Pake doublet. The final expression permits both describing the FID shape of a polymer melt as a function of the molecular mass and temperature below the temperature of the primitive segment quasi-static state and forecasting the temperature range in which oscillating FIDs have been observed for poly(isoprene) melt. The new approach is applicable to qualitatively describe the oscillating FID in semi-crystalline poly(ethylene).

Quantum and Classical Correlations in the Solid-State NMR Free Induction Decay

The free induction decay (FID) of the transverse magnetization in a dipolar-coupled rigid lattice is a fundamental problem in magnetic resonance and in the theory of many-body systems. As it was shown earlier the FID shapes for the systems of classical magnetic moments and for quantum nuclear spin ones coincide if there are many nearly equivalent nearest neighbors n in a solid lattice. In this paper, we reduce a multispin density matrix of above system to a two-spin matrix. Then we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations at the arbitrary spin quantum number S, in the high-temperature approximation. The time dependence of these functions is expressed via the derivative of the FID shape. To extract classical correlations for S > 1/2 we provide generalized POVM measurement (positive-operator-valued measure) using the basis of spin coherent states. We show that in every pair of spins the portion of quantum correlations changes from 1/2 to 1/(S + 1) when S is growing up, and quantum properties disappear completely only if S → ∞.

Influence of Sample Rotation on the Shape of the Free Induction Decay

Sample rotation is commonly used in NMR as one of the methods which improve the effective homogeneity of magnetic fields. The magic angle spinning (MAS), the double rotation (DOR) and the dynamic angle spinning (DAS) can remove line broadening of an NMR spectrum in solids [1, 2]. It is generally assumed that the NMR spectrum of a rotating sample (in the case of isotropic liquids) is simply the orientationally averaged spectum [3]. Our calculations, which are presented below, show that the sample rotation can change the shape of free induction decay (FID) (and consequently NMR line). We discuss this fact because, as we shall show later, it can disturb the absolute evaluation of the measured relaxation time. The shape of the FID can be calculated from the well-known Bloch equation for the transverse component of the magnetization M (without diffusion) under following assumptions [4]:

Low resolution pulse magnetic resonance for measuring moisture in selected grains and kernels

Pulse nuclear magnetic resonance (NMR) was evaluated for usefulness for moisture content measurement in wheat, corn, soybeans, pecans and peanuts. The free induction decay (FID) and in some cases, spin-echo (SE) outputs were used. Moisture content affected the shape of the FID curve, particularly with wheat, corn and soybeans. Relationships between moisture and NMR variables describing FID shape resulted in coefficients of determination ranging from 0·8 to 0·97 for wheat, corn and soybeans. The relatively high oil content of peanuts and pecans probably reduced the FID shape sensitivity to moisture content. Additional studies on peanuts by SE and FID data analysis gave coefficients of determination ranging from 0·8 to 0·9. NMR may be useful for detecting high-moisture kernels or aliquots within batches of grains but appropriate hardware is needed to provide adequate throughput.

Field dependence of 19F NMR in rat bone powders

The 19F NMR properties of fluoridated rat bone powder samples have been studied in several external magnetic fields. The results show a characteristic field dependence, related to the strength of chemical shift interactions compared to dipole-dipole interactions. While the free induction decay shape is relatively insensitive to the 19F bone mineral concentration, the spin-lattice relaxation time decreases with increasing 19F concentration. Multi-exponential spin-lattice relaxation processes indicate that there are at least two chemically inequivalent incorporation sites for fluorine in bone mineral. Evidence for clustering of 19F fluoride impurities in bone mineral is seen in Hahn echo experiments. Sample preparation and handling methods are shown to affect the values of some of the observed NMR parameters.

A method of measuring the initial behavior of the free induction decay

A method for accurately measuring the initial portion of an NMR free induction decay, including a point at t = 0, is described in some detail. Theoretical calculations justifying the technique are carried out. The technique uses spin locking, and is limited to single crystals. The results of free induction decay shape measurements using a single 90° pulse and those using the present technique are found to be identical to within experimental error for 19F in CaF 2 (representing a rigid lattice) and PbF 2 (representing a motionally narrowed lattice).

Nuclear Magnetic Resonance Line-Shape Calculations for a Spin System in a Fixed Lattice

A theoretical formula is derived for the free-induction decay of a system of identical particles of spin I. The exponential terms containing noncommuting operators are expanded by the method used in the paper by Lowe and Norberg. Only enough terms are kept to make the expansion rigorous through ${t}^{4}$. The resulting formula is evaluated for a system of identical particles for which: (1) the spins form a simple cubic lattice, a face-centered cubic lattice, and a body-centered cubic lattice; (2) there is pure magnetic dipole-dipole interaction between the spins; (3) the applied magnetic field is along the [100], [110], and [111] axes of the lattice; (4) $I=\frac{1}{2},1,\frac{3}{2}, \mathrm{and} \ensuremath{\infty}$. The Fourier transforms of the free-induction decays are also plotted. The computations show that the free-induction decay shape is remarkably insensitive to the value of $I$.

The temperature dependence of Lowe-Norberg beats in CaF2

Measurements of the nuclear free induction decay shape in CaF2 show the predicted elimination of Lowe-Norberg beats by phonons at the Debey temperature does not occur. Measurements of diffusion motional relaxation and narrowing at 800 – 1200°K are included.

Effects of Rotating Magnetic Fields on Free-Induction Decay Shapes

The behavior of a set of particles in a rotating magnetic field is analyzed to determine how the lengthening of a nuclear magnetic resonance free- induction decay might occur. An experimert to determine the effect of pulse length on the subsequent free-induction decay was carried out for gypsum, calcium fluoride, and ice. A single r-f pulse at the Larmor frequency of the spin system was applied to the sample in equilibrium and the resulting free-induction decay shape was recorded. The r-f pulse length was varied from 1 to 18 mu sec and the magnetic field ranged from 3 to 30 gauss. (C.E.S.)