DOI: 10.5061/dryad.80gb5mm0t
title: Microstructural geometry revealed by NMR lineshape analysis

description: We introduce a technique for extracting microstructural geometry from NMR
 lineshape analysis in porous materials at angstrom-scale
 resolution with the use of weak magnetic field gradients. Diverging from
 the generally held view of FID signals undergoing simple exponential
 decay, we show that a detailed analysis of the line shape can
 unravel structural geometry on much smaller scales than
 previously thought. While the original q-space PFG NMR relies on strong
 magnetic field gradients in order to achieve high spatial resolution, our
 current approach reaches comparable or higher resolution using
 much weaker gradients. As a model system, we simulated gas diffusion for
 xenon confined within carbon nanotubes over a range of
 temperatures and nanotube diameters in order to unveil
 manifestations of confinement in the diffusion behavior. We report a
 multiscale scheme that couples the above MD simulations with the
 generalized Langevin equation to estimate the
 transport properties of interest for this problem, such as
 diffusivity coefficients and NMR lineshapes, using the Green-Kubo
 correlation function to correctly evaluate time-dependent diffusion. Our
 results highlight how NMR methodologies can be adapted as effective means
 of structural investigation at very small scales when dealing
 with complicated geometries. This method is expected to
 find applications in materials science, catalysis, biomedicine,
 and other areas.
description: <strong>Methods for Data Collection and
 Processing</strong> <strong>1. Molecular
 Dynamics (MD) Simulations:</strong> The primary
 data for this work were generated using Molecular Dynamics (MD)
 simulations conducted with the open-source software package LAMMPS. The
 following steps outline the simulation setup and execution:
 <strong>System Configuration:</strong>
 Carbon nanotubes (CNTs) with radii ranging from 8 Å to 40 Å were
 constructed using a cylindrical lattice arrangement of carbon atoms. Xenon
 (Xe) gas particles were introduced into the CNTs at densities consistent
 with experimental conditions. The number of Xe atoms was adjusted to
 maintain uniform gas density across all CNT geometries.
 <strong>Interaction Potentials:</strong>
 The interactions between Xe atoms were modeled using a
 Lennard-Jones (LJ) potential with parameters \epsilon = 1.77 \,
 \text{kJ/mol} and \sigma = 4.1 \, \text{Å} . Similarly, Xe-CNT
 interactions were described using an LJ potential with \epsilon = 0.71 \,
 \text{kJ/mol} and \sigma = 3.7 \, \text{Å}. The carbon atoms forming the
 CNT walls were held fixed during the simulation.
 <strong>Simulation Parameters:</strong>
 Simulations were performed under periodic boundary conditions
 along the CNT axis to mimic infinite tube lengths. The time step was set
 to 1 femtosecond, and each simulation was run for 10 nanoseconds to
 capture sufficient particle dynamics. Initial conditions, including
 velocities, were generated using a Maxwell-Boltzmann distribution
 corresponding to the specified temperatures (240–400 K).
 <strong>Data Collection:</strong>
 The Green-Kubo autocorrelation function for the pressure tensor
 components was computed directly from the MD simulations. These
 correlation functions provided the foundation for calculating
 time-dependent viscosity and diffusion coefficients. Position and velocity
 data for Xe particles were recorded at regular intervals to enable
 detailed analysis of molecular trajectories.
 <strong>2. Data Processing and
 Analysis:</strong> <strong>Viscosity
 Calculations:</strong> The time-dependent
 viscosity of Xe gas inside CNTs was calculated using the Green-Kubo
 formalism. The pressure tensor autocorrelation function, sampled during
 the MD simulations, was integrated over time to determine the shear
 viscosity \eta(t). Frequency-dependent viscosity \eta(s) was subsequently
 obtained via a numerical Laplace transform.
 <strong>Diffusion Coefficient
 Calculations:</strong> Using the generalized
 Stokes-Einstein equation in the Laplace domain, the diffusion coefficient
 D(s) was computed as a function of frequency. An inverse Laplace transform
 was then applied to recover the time-dependent diffusion coefficient D(t).
 This approach ensured an accurate representation of memory effects and
 time-dependent transport properties. <strong>NMR
 Lineshape Predictions:</strong> The time-domain
 diffusion coefficients were incorporated into the generalized Langevin
 equation (GLE) framework to predict NMR lineshapes. By combining
 MD-derived parameters with the GLE, we successfully modeled signal
 attenuation and lineshape broadening as functions of molecular transport
 and confinement effects. <strong>Validation and
 Sensitivity Analysis:</strong> The results were
 validated by comparing simulated data to theoretical expectations and
 trends reported in the literature. Sensitivity analyses were conducted to
 ensure the robustness of the results with respect to simulation
 parameters, such as tube radius, temperature, and gas density.
 <strong>3. Data Accessibility:</strong>
 The database includes: <strong>Raw MD
 Simulation Data:</strong> • Positions and
 velocities of all Xe particles recorded during simulations.
 • Pressure tensor components used to calculate Green-Kubo
 autocorrelation functions. <strong>Processed Data
 Files:</strong> • Time-dependent viscosity and
 diffusion coefficients derived from the Green-Kubo approach.
 • Frequency- and time-dependent diffusion data used for NMR
 lineshape modeling. <strong>Analysis
 Scripts:</strong> • Python scripts for computing
 autocorrelation functions, viscosity, and diffusion
 coefficients. • Numerical Laplace and inverse Laplace
 transform scripts for processing frequency-domain data.
 • GLE-based NMR lineshape modeling code.
description: # Microstructural geometry revealed by NMR lineshape analysis
 [https://doi.org/10.5061/dryad.80gb5mm0t](https://doi.org/10.5061/dryad.80gb5mm0t) ## Description of the data and file structure This dataset supports the analysis presented in the paper, *“Microstructural Geometry Revealed by NMR Lineshape Analysis”* (Niknam & Bouchard, [https://arxiv.org/abs/2410.09700](https://arxiv.org/abs/2410.09700)). The files include simulation input scripts, raw output data, logs, visual snapshots, and analysis notebooks for studying the molecular diffusion of xenon (Xe) gas inside confined carbon nanotubes (CNTs). A visualization movie of the diffusion process is also included to help interpret the results. ## **Contents** #### **1. Simulation Input Files** **Description**: Input files for running LAMMPS molecular dynamics (MD) simulations. **Files**: in.visc_cnt: LAMMPS input script to compute viscosity and simulate particle dynamics in CNTs. nanotube.data: Data file specifying the atomic configuration of the CNT structure. generate_nanotube.lmp: Script for generating CNT configurations with specified radii and dimensions. submit_job.sh: Example job submission script for running simulations on an HPC cluster. #### **2. Simulation Output Files** **Description**: Outputs generated during the LAMMPS simulations. **Files**: log.lammps: Contains detailed simulation logs, including energy outputs (kinetic, potential, total energy) and thermodynamic quantities at each time step. dump.comp.980000: Snapshot of atomic positions and velocities at a specific timestep. These frames can be used to visualize the molecular configuration of Xe atoms inside the CNT. #### **3. Visualization Files** **Description**: Visualization outputs illustrating the molecular diffusion of Xe gas in the CNT. **Files**: XeDiffCNT20A.mp4: A movie showing the diffusion of Xe atoms within a carbon nanotube (radius = 20 Å).  The movie was generated using snapshots (like dump.comp.980000) to provide a dynamic visualization of the simulation results. #### **4. Data Analysis** **Description**: Jupyter Notebook containing Python scripts for post-simulation analysis. **Files**: paper3analysis.ipynb: Calculates viscosity using Green-Kubo formalism from pressure tensor data. Computes time- and frequency-dependent diffusion coefficients using numerical Laplace transforms. Models NMR lineshapes using generalized Langevin equation (GLE)-based analysis. Includes scripts for visualizing viscosity trends, diffusion coefficients, and NMR signal attenuation. ## **Simulation Details** #### 1. **System Configuration**: Carbon nanotubes (CNTs) of specified radii were constructed using generate_nanotube.lmp. Xenon (Xe) gas particles were simulated within CNTs at densities consistent with experimental conditions. #### 2. **Simulation Parameters**: Software: LAMMPS. Interaction potentials: Lennard-Jones (LJ) potential for Xe-Xe and Xe-CNT interactions. Time step: 1 femtosecond. Total simulation time: 10 nanoseconds. Thermodynamic data (energy, temperature, etc.) was logged every 1000 steps in log.lammps. #### 3. **Visualization**: rames like dump.comp.980000 were used to visualize the molecular configurations. The movie XeDiffCNT20A.mp4 illustrates the dynamic behavior of Xe atoms diffusing within the CNT. ## **Data Processing** #### 1. **Viscosity Calculation**: Green-Kubo formalism was applied to pressure tensor autocorrelation functions. #### 2. **Diffusion Coefficient Calculation**: frequency-dependent diffusion coefficients were derived using the generalized Stokes-Einstein equation and numerical Laplace transforms. #### 3. **NMR Lineshape Analysis**: GLE-based models were used to predict NMR signal attenuation and broadening effects in confined systems. ## **How to Use the Dataset** #### 1. **Run Simulations**: Use the input files (in.visc_cnt, nanotube.data, generate_nanotube.lmp) to reproduce molecular dynamics simulations in LAMMPS. #### 2. **Analyze Results**: Open paper3analysis.ipynb in Jupyter Notebook. Modify file paths to point to the raw data files (log.lammps, dump.comp.980000) and process the results. #### 3. **Visualize Data**: Use tools like OVITO or VMD to visualize dump files (dump.comp.980000). Play XeDiffCNT20A.mp4 to observe the molecular diffusion process. #### 4. **Extend Analysis**: The provided scripts can be adapted to analyze different systems or geometries by modifying input files and parameters. ## **Citation** If you use this dataset or scripts in your work, please cite: [https://arxiv.org/abs/2410.09700](https://arxiv.org/abs/2410.09700) Niknam, M. & Bouchard, L.-S. (2024). *Microstructural Geometry Revealed by NMR Lineshape Analysis*. ### Files and variables #### File: submit\_job.sh **Description:** Example job submission script for running simulations on an HPC cluster. #### File: in.visc\_cnt **Description:** LAMMPS input script to compute viscosity and simulate particle dynamics in CNTs. #### File: generate\_nanotube.lmp **Description:** Script for generating CNT configurations with specified radii and dimensions. #### File: paper3analysis.ipynb **Description:** Jupyter Notebook containing Python scripts for post-simulation analysis. #### File: log.lammps **Description:** Contains detailed simulation logs, including energy outputs (kinetic, potential, total energy) and thermodynamic quantities at each time step. #### File: dump.comp.980000 **Description:** Snapshot of atomic positions and velocities at a specific timestep. #### File: nanotube.data **Description:** Data file specifying the atomic configuration of the CNT structure. #### File: cnt\_viscg\_320\_20.dat **Description:** An example of the simulation output, temp: 320K and CNT radius: 20 \AA ## Code/software **1. Software for Viewing and Running Data** **LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator)** **Description**: LAMMPS is an open-source molecular dynamics (MD) simulator widely used for modeling materials at the atomic scale. **Version**: LAMMPS version 29 Oct 2020 was used for generating the simulation data. **Files**: Input scripts: in.visc_cnt, generate_nanotube.lmp, and nanotube.data. Outputs: log.lammps (simulation log) and dump.comp.980000 (snapshots of atomic positions). **Workflow**: LAMMPS runs the provided input files to simulate the molecular dynamics of xenon gas in CNTs. The generate_nanotube.lmp script generates CNT configurations, and in.visc_cnt runs simulations with output data stored in dump.comp.980000 and logs in log.lammps. **Download**: [LAMMPS Official Site](https://lammps.org/) **Jupyter Notebook (Python)** **Description**: Jupyter Notebook is an open-source interactive computing tool for running and documenting Python code. **Version**: Jupyter Notebook version 6.4.12. **Key Packages**: numpy (v1.21.0): Numerical operations and array processing. scipy (v1.7.0): Used for numerical Laplace and inverse Laplace transforms. pandas (v1.3.0): For managing and processing tabular data. matplotlib (v3.4.3): For visualizing viscosity trends, diffusion coefficients, and NMR lineshapes. **Files**: paper3analysis.ipynb: Jupyter Notebook that processes simulation outputs, computes transport properties, and generates plots. Input files for analysis: cnt_viscg_320_20.dat, dump.comp.980000, and log.lammps. **Workflow**: 1\. Load MD simulation outputs (e.g., pressure tensor and atomic positions). 2\. Compute viscosity using the Green-Kubo formalism. 3\. Derive diffusion coefficients using Laplace transforms. 4\. Predict NMR lineshapes using the generalized Langevin equation (GLE). 5\. Visualize results using matplotlib. **Download**: [Jupyter Project](https://jupyter.org/) **OVITO (Open Visualization Tool)** **Description**: OVITO is an open-source tool for visualizing and analyzing molecular dynamics simulation data. **Version**: OVITO version 3.6.0. **Files**: dump.comp.980000: Atomic snapshots from the LAMMPS simulation. **Workflow**: Use OVITO to load the dump files and visualize the molecular arrangement of xenon gas inside the CNT. ## Access information NA