^{1}, Lela Vukovic

^{2}and Cynthia J. Jameson

^{2,a)}

### Abstract

To make predictions of the Xe NMR line shapes for Xe in channels decorated with paramagnetic centers, we consider a model system using the molecule as the paramagnetic center. The previously calculated quantum mechanical hyperfinetensor for various configurations of Xe in the presence of provides a model for the hyperfine response of Xe atom to the presence of a paramagnetic center. The averaging is carried out using the same grand canonical Monte Carlo methodology as for calculating NMR line shapes for Xe in diamagnetic channels, modified to include the effects of the hyperfinetensor response. We explore the temperature dependence of the Xe line shapes, the dependence on the concentration, and the symmetry of distribution of embedded paramagnetic centers, on the orientation of the paramagnetic center axis with respect to the channel axis, and on the radial distance of the paramagnetic center from the axis of the channel. We predict Xe line shape signatures of the presence and orientation of paramagnetic centers and deduce which tensor elements provide measures of concentration and radial distance of paramagnetic centers from the channel axis.

This work has been supported in part by the National Science Foundation (Grant No. CHE-9979259). D.N.S. thanks the Alberta Ingenuity Fund and the I. W. Killam Fund for postdoctoral fellowships. L.V. is grateful for the Herbert E. Paaren Scholarship during the course of this work at UIC.

INTRODUCTION

METHODOLOGY

The model system

The Xe shielding response and the hyperfine response functions

The diamagnetic shielding response tensor from interactions of Xe with the channel atoms

The diamagnetic shielding response tensor from the paramagnetic center

The Fermi contact contribution from the paramagnetic center

The hyperfine dipolar contribution from the paramagnetic center

The bulk magnetic susceptibility contribution

The potential functions needed for averaging

RESULTS

The diamagnetic channel without the paramagnetic centers

The concentration of paramagnets

The orientation of paramagnets

The distribution of paramagnets within the channel

The distribution of paramagnets in the solid

Xe occupancy

The average distance from the paramagnet

The isotropic chemical shift

SUMMARY OF Xe LINE SHAPE SIGNATURES

DISCUSSION

CONCLUSIONS

### Key Topics

- Paramagnetism
- 133.0
- Tensor methods
- 79.0
- Chemical shifts
- 43.0
- Diamagnetism
- 43.0
- Hyperfine structure
- 23.0

## Figures

The supercells constructed for model systems used in this work (the simulation box). All have the same paramagnet to framework atom ratio. The dark atoms are the C–C units in the original carbon nanotube which have been replaced by ; the dots are dummy atoms placed between nanotubes to prevent the Xe atoms from being created in interstitial positions. The lines delineate the unit cells. All views, except for model A are looking down the c axis of the crystal. The side view of model A shows the -doping pattern (one ring per unit cell). The four molecules are arranged in a ring so as to have the axis of the paramagnetic center parallel to the channel axis. All the models shown in this figure have the -doping pattern seen in the side view of model A, i.e., one ring per unit cell. Model B has the same arrangement, and the same distribution within the channel as in model A, but the distribution within the crystal is different from model A. Model C has the same distribution of paramagnetic centers as model B, but the axes of the paramagnetic centers are perpendicular to the channel axis. Model D channels have smaller diameter, and the same parallel orientation of paramagnetic centers as model B; there are three molecules arranged in a ring. Model H channels have larger diameters, and the same parallel orientation of paramagnetic centers as model B; there are five molecules arranged in a ring.

The supercells constructed for model systems used in this work (the simulation box). All have the same paramagnet to framework atom ratio. The dark atoms are the C–C units in the original carbon nanotube which have been replaced by ; the dots are dummy atoms placed between nanotubes to prevent the Xe atoms from being created in interstitial positions. The lines delineate the unit cells. All views, except for model A are looking down the c axis of the crystal. The side view of model A shows the -doping pattern (one ring per unit cell). The four molecules are arranged in a ring so as to have the axis of the paramagnetic center parallel to the channel axis. All the models shown in this figure have the -doping pattern seen in the side view of model A, i.e., one ring per unit cell. Model B has the same arrangement, and the same distribution within the channel as in model A, but the distribution within the crystal is different from model A. Model C has the same distribution of paramagnetic centers as model B, but the axes of the paramagnetic centers are perpendicular to the channel axis. Model D channels have smaller diameter, and the same parallel orientation of paramagnetic centers as model B; there are three molecules arranged in a ring. Model H channels have larger diameters, and the same parallel orientation of paramagnetic centers as model B; there are five molecules arranged in a ring.

The supercells for the model systems which have twice the concentration of paramagnetic centers compared to corresponding models in Fig. 1. All have four molecules arranged in a ring. Model E has the same parallel arrangement of paramagnetic centers as model B, with the four molecules stacked vertically every level rather than every other level. Model F has the same parallel arrangement of paramagnetic centers as model E, but the positions of the four units rotate at each level producing a helical pattern. Model G has the same perpendicular orientation of paramagnetic centers as model C.

The supercells for the model systems which have twice the concentration of paramagnetic centers compared to corresponding models in Fig. 1. All have four molecules arranged in a ring. Model E has the same parallel arrangement of paramagnetic centers as model B, with the four molecules stacked vertically every level rather than every other level. Model F has the same parallel arrangement of paramagnetic centers as model E, but the positions of the four units rotate at each level producing a helical pattern. Model G has the same perpendicular orientation of paramagnetic centers as model C.

The Xe line shapes for Xe-channel interactions (in the limit of zero Xe occupancy) at 300, 250, and in the neon nanotube doped with in model B (bottom) compared with the Xe line shapes under the same conditions, but with the coefficients of all hyperfine terms zeroed out, i.e., in the absence of hyperfine effects (top).

The Xe line shapes for Xe-channel interactions (in the limit of zero Xe occupancy) at 300, 250, and in the neon nanotube doped with in model B (bottom) compared with the Xe line shapes under the same conditions, but with the coefficients of all hyperfine terms zeroed out, i.e., in the absence of hyperfine effects (top).

The effect of concentration and the distribution of paramagnetic centers. (a) Xe line shapes for Xe-channel interactions (in the limit of zero Xe occupancy) at 300, 250, and in the neon nanotube doped with in model E (top) which has twice the concentration of paramagnetic centers as model B in Fig. 3. (b) Xe line shapes in model A (bottom) which have the same concentration and arrangement of paramagnetic centers within the channel as model B in Fig. 3, but the distribution of paramagnets in the solid is different.

The effect of concentration and the distribution of paramagnetic centers. (a) Xe line shapes for Xe-channel interactions (in the limit of zero Xe occupancy) at 300, 250, and in the neon nanotube doped with in model E (top) which has twice the concentration of paramagnetic centers as model B in Fig. 3. (b) Xe line shapes in model A (bottom) which have the same concentration and arrangement of paramagnetic centers within the channel as model B in Fig. 3, but the distribution of paramagnets in the solid is different.

The axis of the paramagnetic center is perpendicular to the axis of the channel. Line shapes in model C (top) are compared with line shapes in model G which has twice the concentration of paramagnetic centers (bottom).

The axis of the paramagnetic center is perpendicular to the axis of the channel. Line shapes in model C (top) are compared with line shapes in model G which has twice the concentration of paramagnetic centers (bottom).

The Xe line shapes as a function of Xe occupancy. Xe line shapes in the neon nanotube doped with in model B at (right) are compared with the line shapes under the same conditions, but with the coefficients of all hyperfine terms zeroed out, i.e., in the absence of hyperfine effects (left). The fractional occupancy .

The Xe line shapes as a function of Xe occupancy. Xe line shapes in the neon nanotube doped with in model B at (right) are compared with the line shapes under the same conditions, but with the coefficients of all hyperfine terms zeroed out, i.e., in the absence of hyperfine effects (left). The fractional occupancy .

The effect of the channel diameter. The Xe line shapes for Xe-channel interactions (in the limit of zero Xe occupancy) are compared in the -doped neon nanotubes of increasing diameter in models H, B, and D at 300 (top) and at (bottom).

The effect of the channel diameter. The Xe line shapes for Xe-channel interactions (in the limit of zero Xe occupancy) are compared in the -doped neon nanotubes of increasing diameter in models H, B, and D at 300 (top) and at (bottom).

## Tables

The hyperfine contributions to the Xe chemical shift tensor in each of the model systems.

The hyperfine contributions to the Xe chemical shift tensor in each of the model systems.

The Fermi contact contributions to the isotropic Xe chemical shift in each of the model systems.

The Fermi contact contributions to the isotropic Xe chemical shift in each of the model systems.

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