The Living Cell as a Physical System
Cell biology sits at the intersection of chemistry, physics, and information theory. The cell membrane is a lipid bilayer roughly 5 nm thick — yet it maintains electrical potentials up to 100 mV across it, sorts thousands of molecular species, and transmits signals at speeds approaching electrical cables. Three simulations now cover the main physical frameworks:
Cytoskeleton
Dynamic instability of actin filaments and microtubules: polymerisation, catastrophe, and the treadmilling steady state.
Explore →Cell Signalling
Receptor activation, second-messenger cascades (cAMP, Ca²⁺), and signal amplification through kinase phosphorylation networks.
Explore →Membrane Transport
Ion channels, the Na⁺/K⁺-ATPase pump, and the Goldman-Hodgkin-Katz equation linking permeability ratios to membrane potential.
Explore →The Goldman-Hodgkin-Katz Equation
Most students first meet the Nernst equation, which gives the equilibrium potential for a single ion species: E_ion = (RT/zF) · ln([X]_out / [X]_in). But real membranes are permeable to multiple ions simultaneously. The GHK voltage equation extends this by weighting each ion’s contribution by its relative permeability:
V_m = (RT/F) ln[(P_Na[Na]_out + P_K[K]_out + P_Cl[Cl]_in) / (P_Na[Na]_in + P_K[K]_in + P_Cl[Cl]_out)]
The inverted placement of Cl⁻ concentrations reflects the sign of its charge — a common source of confusion in textbooks. At rest, K⁺ permeability dominates and V_m ≈ −70 mV. When voltage-gated Na⁺ channels open during an action potential, the P_Na/P_K ratio jumps from about 0.02 at rest to over 20 transiently, and V_m swings to near +35 mV before K⁺ channels restore the resting potential.
Molecules in Bulk — Beyond Ideal Behaviour
Physical chemistry provides the quantitative bridge between atomic/molecular properties and macroscopic thermodynamic observables. Three simulations now cover spectroscopy, surface science, and real-gas thermodynamics:
Molecular Spectroscopy
Rotational and vibrational energy levels, selection rules, and the origin of IR and Raman spectra from quantum-mechanical transitions.
Explore →Adsorption Isotherm
Langmuir and BET adsorption: surface coverage vs pressure, monolayer capacity, and the physics of porous material characterisation.
Explore →Van der Waals Gas
Real-gas P-V isotherms, Maxwell equal-area construction, the liquid-vapour critical point, and the law of corresponding states.
Explore →Why Ideal Gases Fail Near Phase Transitions
The ideal gas law PV = nRT predicts that isotherms are simple hyperbolas and that there is no phase transition — a gas smoothly and continuously becomes a liquid as pressure rises. This is obviously wrong: water at 99 °C boils abruptly at 1 atm. The van der Waals correction captures this by introducing two parameters:
- a — intermolecular attraction, which reduces pressure by a/V_m²
- b — excluded volume (four times the hard-sphere volume per molecule)
Below T_c, the VdW cubic has three positive real roots. The outermost (smallest V, highest P) is the liquid spinodal; the innermost (largest V) is the vapour spinodal. The middle root is mechanically unstable. The physical coexistence pressure is found by the equal-area (Maxwell) condition: the loop area above and below the horizontal tie line must be equal. This is equivalent to requiring equal chemical potential in both phases.
For water: T_c = 647 K, P_c = 221 bar, V_c/n = 91.6 mL/mol. For He: T_c = 5.2 K (helium is quantum and barely condenses at all at atmospheric pressure). The same Maxwell equation applies — just at vastly different scales.
Processing, Microstructure, Properties
The central paradigm of materials science is the processing-microstructure-properties triangle: the way you make a material determines its internal structure, which determines its mechanical, electrical, and thermal behaviour. Three simulations now span atomic diffusion, shape memory, and grain growth:
Crystal Diffusion
Vacancy-mediated atomic diffusion in a crystal lattice: Fick’s laws, concentration profiles, and the Arrhenius temperature dependence of the diffusion coefficient.
Explore →Shape Memory Alloy
Martensitic phase transformation in Ni-Ti: thermoelastic martensite, superelasticity above A_f, and the two-way shape-memory effect.
Explore →Grain Growth
Voronoi metallic microstructure coarsening during annealing. Parabolic growth law + Hall-Petch: watch yield strength fall as grains grow.
Explore →The Hall-Petch Relation in Practice
Hall-Petch strengthening is one of the most practically important results in metallurgy. All else equal, halving the mean grain diameter d̄ increases yield strength by a factor of √2 ≈ 1.41. For low-carbon steel with k_HP = 0.74 MPa·m^½, going from d̄ = 100 µm to 10 µm raises σ_y from ~180 to ~380 MPa — more than doubling the strength purely by microstructural refinement, with no change in composition or crystal structure.
The practical limit is nanocrystalline regime (d̄ < 10 nm), where grain boundary sliding becomes the dominant deformation mechanism and Hall-Petch breaks down — strength actually decreases for the finest grain sizes. This “inverse Hall-Petch” effect is an active research area in nanostructured materials.