Introduction

Diffusive transport, also called mass transfer, plays important roles in both natural and industrial processes. In biological systems, the transfer of oxygen and nutrients from blood vessels to tissue cells occurs by diffusion. In industry, many separations processes operate by diffusion: e.g., distillation is based on diffusion between a liquid and vapor phase, and liquid-liquid extraction is based on the diffusion of a solute between two immiscible phases.

What property controls how diffusion will proceed? A common misconception is that diffusion is controlled by concentration gradients; however, this dependence occurs only in special circumstances. More generally, diffusion is controlled by gradients of the chemical potential, such that molecules diffuse from regions of higher chemical potential to regions of lower chemical potential. Net diffusion stops when chemical potential gradients are erased.

This module presents an interactive molecular simulation that shows how diffusion is related to the chemical potential, and how the chemical potential depends on factors such as concentration, pressure, temperature and molecular properties. The dynamics of a sample of molecules are simulated by numerically solving Newton’s laws of motion, and animations of the molecular trajectories are shown. System properties relevant to the chemical potential are calculated from these trajectories, and displayed both graphically and numerically. The user can change the conditions (concentration, density and pressure), and how the molecules interact with each other, to see how these changes affect the chemical potential and molecular diffusion.

An underlying theme of this module is the relationship of the chemical potential of real systems to that of an ideal gas. In standard thermodynamic formalisms, the chemical potential of a real system is considered as a perturbation of the ideal gas result, where the magnitude of the perturbation is described by the fugacity coefficient. To explicitly address this relationship, the module simulates a phase composed of ‘real’ molecules that interfaces with an ideal gas phase in which the molecules do not interact; the molecules freely pass through the interface between these phases, and net diffusion between the phases occurs until equilibrium is reached. In this way the simulation shows how the properties of the real system compare to that of an ideal gas. In particular, the fugacity of a species in a fluid is equal to the partial pressure of the species in an ideal-gas phase in equilibrium with the fluid.

This module is geared towards students in undergraduate and graduate courses in thermodynamics and physical chemistry.