Simulation Playground

Three inspectable molecular experiments: pair structure in a bulk fluid, melting hysteresis and coexistence in iron, and molecular layering inside a nanopore. Choose a condition, run a fixed protocol, and compare measured observables.

A repeatable browser experiment

Ask one question. Measure one answer.

Start from a named condition, keep the random seed fixed, and let the model complete the same protocol each time. Save a control, alter one independent variable, then compare the measured curves—not an instantaneous frame.

01ChooseSelect the physical question and baseline condition.
02MeasureEquilibrate, then sample a fixed observation window.
03CompareChange one variable and inspect the response.

Bulk pair structure

A two-dimensional Lennard–Jones fluid with temperature and density exposed. Run a fixed sampling window and read molecular coordination from the radial distribution function g(r).

N = — T = — K T* = — steps/s = —

Fig. — Velocity-Verlet integration with a Berendsen thermostat, identical algorithm to the homepage hero. Drag your cursor through the fluid to perturb it. The engine runs in reduced units; temperatures are shown in Kelvin using argon's well depth (ε/k_B = 120 K).

Radial distribution function

g(r) — fixed-window pair correlation. Amber is the current result; blue is saved control A.

Ready. Controls define the setup; no measurement has been collected.

Reading pair structure

What the RDF reveals

At low temperature and moderate-to-high density, g(r) develops peaks near r ≈ σ, √3·σ, and 2σ—the first coordination shells of a locally ordered two-dimensional fluid. Their positions describe preferred neighbour distances; their height describes how strongly those distances are selected.

As temperature rises, the peaks soften toward g(r) → 1, indicating a disordered fluid with no preferred long-range separation. This browser model is a transparent companion to the published confined-fluid simulations: read the exact record.

Iron melting

Heat bcc iron from 1000 K to 2600 K in 500,000 MD steps, then cool it back to 1000 K in another 500,000. A compact retained bcc nucleus seeds crystallization during cooling; each measured point averages 1,000 consecutive steps.

stage = ready T = — K PE = — J/atom bcc = — t = 0.0 ps

Fig. — Schematic atom positions keyed to the measured CNA bcc fraction. Blue atoms are bcc-like; amber atoms are unclassified/liquid-like. The graph—not this rendering—is the quantitative measurement.

Graph observable

Question: Where do melting and seeded crystallization occur during a finite-rate cycle?
Look for: an upward jump on heating and a downward jump as bcc order grows on cooling.

cycle = 1000 → 2600 → 1000 K each leg = 500,000 steps point = 1,000-step mean pressure = 0 GPa timestep = 1 fs

Potential energy is in joules per atom. Time still advances in the readout, but temperature makes the transition locations directly readable.

Why seed the cooling leg? An unseeded rapid quench became amorphous because homogeneous nucleation was slower than the run. A compact 18-atom bcc nucleus supplies an interface without the excessive solid bias produced by a full pinned layer.

Potential energy hysteresis

Faint lines show every 1,000-step PE mean; bold lines show a centered 21-block (21,000-step) rolling mean in joules per atom.

Reference data loading.

Reading a first-order transition

How the melting estimate is read

1. Follow the amber heating curve. Its sharp upward discontinuity is T⁺, where most of the crystal melts around the retained seed. 2. Follow the blue cooling curve. Its downward discontinuity is the seeded cooling transition T⁻; the simultaneous rise in CNA bcc fraction confirms crystal growth rather than a purely thermal energy change.

3. Use solid–liquid coexistence for the equilibrium answer. Start with both phases already present: below T_m solid grows, above T_m liquid grows. The dashed green line is the longer NIST two-phase result for this potential, 1767.99 ± 1.85 K; experimental pure iron is near 1811 K. NIST potential and computed properties ↗

Potential: Mendelev et al. Fe #2, EAM/fs.
Integration: 432 atoms, periodic 6×6×6 bcc cell, velocity Verlet, 1 fs; 500,000 steps per leg.
Nucleation seed: A compact retained bcc nucleus, 18 atoms. It promotes reproducible cooling crystallization without pinning an entire periodic layer.
Control: NPT at 0 GPa; Nose–Hoover T-damping 100 fs and P-damping 1000 fs.
Sampling: 500 points per leg; each measured point averages temperature, PE, volume, and bcc count across 1,000 steps.
Hysteresis diagnostic: T_m,hys = T⁺ + T⁻ − √(T⁺T⁻). It remains rate- and seed-dependent; the two-phase value is the equilibrium reference.

Nanopore confinement

Confine coarse-grained ethane between parallel graphene sheets and its packing becomes strongly position-dependent. The companion plot is the normalised density profile ⟨ρ(z)⟩/ρ̄ collected over a fixed sampling window after equilibration.

N_mol = — H = — layers = — samples = 0 / 4,000

⟨ρ(z)⟩ / ρ̄

wall → wall

Fig. — Coarse-grained ethane in a graphene slit pore, periodic laterally. Each C₂H₆ glyph follows a Lennard-Jones centre of mass; the graphene sheets use an integrated 9-3 wall potential. The measured profile uses a fixed post-equilibration window, and the dashed line marks ρ(z) = ρ̄.

Nanopore question

Question: Do adsorbed layers overlap across a narrow pore?
Expected observable: persistent oscillations with no flat bulk-like centre.

Pore width H9.0σ

Temperature50 K · T* 0.417

Wall/fluid attraction ε_w/ε_ff0.8

Temperature T* = 0.417Seed —

Deterministic seed

Narrow the pore. The layers span the whole gap, so the fluid never recovers its bulk structure.

Raise wall attraction. The contact layer grows: a wetting, adsorbing surface. At zero attraction, contact depletion appears instead.

Ready. Controls define the setup; no measurement has been collected.

Reading a confined fluid

Why confinement changes everything

In a bulk fluid, ρ(z) is flat because every position is equivalent. Bring two walls within a few molecular diameters and that symmetry breaks: molecules pack into layers beside each surface; in a narrow gap those layers meet, leaving no bulk-like centre.

That structural change shifts adsorption, transport, and phase behaviour—the reason gas in a shale-scale pore cannot be read with a bulk equation of state alone. This interactive model is a small, inspectable companion to the site’s work on nanopore fluid behavior in shale.

Wide pore: A central region can recover bulk-like density.
Narrow pore: Layering spans the gap and the profile remains oscillatory.
Stronger wall: Contact density rises as the surface becomes more wetting.