Methane Self-Diffusion Study

A trajectory-analysis workflow for converting molecular motion into mean-squared displacement, diffusion coefficients and finite-size-corrected transport data.

Python
Unwrapped trajectories
Mean-squared displacement
Finite-size correction

Compare unwrapped trajectories 400 K · 358.4 kg/m³

Analysis method Multiple time origins for mean-squared displacement

System-size study 362, 750 and 1,500 methane molecules

Production states 200, 300 and 400 K at 358.4 kg/m³

Related solver

Built on the methane MD solver

This study extends the verified NVT solver with unwrapped position output and a dedicated post-processing workflow.

View Project 02

Trajectory method

Motion without periodic wrapping

Unwrapped coordinates preserve the true displacement of every molecule as it crosses a periodic boundary.

Store origins

Position snapshots become time origins at a fixed sampling frequency.

Accumulate motion

Particle displacements are evaluated over many correlation-time windows.

Average MSD

Squared displacements are averaged across molecules and available time origins.

Fit diffusion

The long-time linear region is converted into a self-diffusion coefficient.

Einstein relation 1 6 d⟨|r(t) − r(0)|²⟩ dt

Mean-squared displacement

Diffusion emerges from the long-time slope

The logarithmic MSD response becomes nearly linear at long correlation times.

A multi-origin algorithm improves statistical use of the trajectory by reusing many time origins instead of relying on one initial frame.

Mean-squared displacement shown on logarithmic axes — Long-time MSD provides the slope used in the Einstein relation.

Finite-size study

Measuring the box-size effect

Three particle counts were simulated at the same density and temperature to test the effect of periodic box size.

Mean-squared displacement for 362, 750 and 1500 methane molecules — The three MSD curves are nearly coincident.

Self-diffusion coefficient plotted against inverse box size — A small residual dependence remains after extracting the slope.

Raw and corrected self-diffusion coefficients plotted against inverse box size — The correction increased the trend at 150 K rather than collapsing it.

Engineering interpretation

The result was treated as a model-diagnostics finding. It shows that the correction is sensitive to the viscosity input and the consistency between the molecular model and the external fluid property.

Mean-squared displacement of methane at 200, 300 and 400 kelvin — Molecular displacement increases consistently with temperature.

Temperature dependence

Faster motion at higher temperature

The 400 K trajectory produces the highest MSD and the 200 K trajectory the lowest.

This monotonic trend carries through to the extracted self-diffusion coefficients.

Literature comparison

Transport results against published values

Corrected diffusion values follow the expected temperature trend and remain closest to the literature values at 200 and 400 K.

Simulated and literature methane self-diffusion coefficients at 200, 300 and 400 kelvin — Corrected simulation values compared with temperature-matched literature estimates.

200 K 17.78 Literature · 17.01

Approximately 4.6% higher.

300 K 25.71 Literature · 22.56

Approximately 14.0% higher.

400 K 33.63 Literature · 32.10

Approximately 4.8% higher.

Diffusion coefficients shown in 10⁻⁹ m²/s.

Engineering outcome

From trajectories to validated transport data

The project extended a custom MD solver into a complete transport-property workflow.

It combined unwrapped trajectory output, multi-origin MSD, finite-size analysis, correction diagnostics and comparison with published methane data.

Trajectory post-processing
Einstein relation
Finite-size analysis
Literature validation