.. _lennard-jones-label: Lennard-Jones fluid =================== .. container:: hatnote Measuring the NMR relaxation time from a Lennard-Jones fluid MD system --------- .. image:: ../figures/illustrations/lennard-jones-fluid/snapshot-dark.png :class: only-dark :alt: LJ fluid simulated with LAMMPS - Dipolar NMR relaxation time calculation :width: 250 :align: right .. image:: ../figures/illustrations/lennard-jones-fluid/snapshot-light.png :class: only-light :alt: LJ fluid simulated with LAMMPS - Dipolar NMR relaxation time calculation :width: 250 :align: right .. container:: justify The system is made of 1638 particles interacting through the classical Lennard-Jones (LJ) 12-6 potential with a cut-off of :math:`9\,\text{Å}`. Each particle was associated with a mass :math:`m = 1\,\text{g/mol}`, and LJ parameters :math:`\sigma = 3\,\text{Å}` and :math:`\epsilon = 0.1\,\text{kcal/mol}`. The volume of the box :math:`(37.5\,\text{Å})^3` was chosen to match the density of the paper by Grivet :cite:`grivetNMRRelaxationParameters2005`. Calculations were made at constant volume and energy, in the NVE ensemble. The total duration of the simulation was 11000 steps, and the data were recorded every 10 steps with a timestep of :math:`1.16\,\text{fs}`. The imposed temperatures were ranging from :math:`T = 30` to :math:`160\,\text{K}`. .. container:: justify The parameters were chosen to match the reduced parameters used by Grivet :cite:`grivetNMRRelaxationParameters2005`, namely a reduced temperature ranging from :math:`T^* = 0.8` to 3.0, a density :math:`\rho^* = 0.84`. Note however, a smaller number of particles was used, as well as a smaller timestep, and a slightly longer cut-off. Results ------- .. container:: justify The correlation function :math:`G^{(0)}` was first extracted for two temperatures, :math:`T = 50` and :math:`140\,\text{K}`, and compared with the correlation functions reported by Grivet :cite:`grivetNMRRelaxationParameters2005`. Our results show an excellent agreement with the results from Grivet, thus validating the NMR formalism used here as well as the LJ system and parameters. .. image:: ../figures/illustrations/lennard-jones-fluid/G_correlation-dark.png :class: only-dark :alt: NMR results obtained from the LAMMPS simulation of water .. image:: ../figures/illustrations/lennard-jones-fluid/G_correlation-light.png :class: only-light :alt: NMR results obtained from the LAMMPS simulation of water .. container:: figurelegend Figure: Correlation function :math:`G^{(0)}` as extracted from the LJ fluid simulation for two different temperatures, and compared with the data from Grivet :cite:`grivetNMRRelaxationParameters2005` (open symbols). .. container:: justify The NMR relaxation rates :math:`R_1` and :math:`R_2` was also extracted for all the temperatures, at a frequency :math:`f_0 = 150\,\text{GHz}`. Our results show a good agreement with the data from Grivet :cite:`grivetNMRRelaxationParameters2005`. .. image:: ../figures/illustrations/lennard-jones-fluid/R1_spectra-dark.png :class: only-dark :alt: NMR results obtained from the LAMMPS simulation of water .. image:: ../figures/illustrations/lennard-jones-fluid/R1_spectra-light.png :class: only-light :alt: NMR results obtained from the LAMMPS simulation of water .. container:: figurelegend Figure: NMR relaxation rates :math:`R_1` and :math:`R_2` at a frequency :math:`f_0 = 150\,\text{GHz}`. The data from Grivet :cite:`grivetNMRRelaxationParameters2005` are shown with open symbols.