Related Experiment Video
Updated: May 18, 2026
06:55
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Nonequilibrium cluster diffusion during growth and evaporation in two dimensions
Yukio Saito1, Matthieu Dufay, Olivier Pierre-Louis
1Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan.
Physical Review Letters
|September 26, 2012
Summary
This study reveals three distinct diffusion regimes for 2D clusters under nonequilibrium conditions. Mean square displacement (MSD) shows unique behaviors during evaporation and growth, differing from equilibrium dynamics.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- The diffusion of two-dimensional (2D) clusters is crucial in various physical phenomena.
- At equilibrium, the mean square displacement (MSD) of a cluster's center of mass scales linearly with time.
- Understanding nonequilibrium dynamics is essential for describing real-world processes.
Purpose of the Study:
- To investigate the diffusion dynamics of growing or evaporating 2D clusters under nonequilibrium conditions.
- To identify and characterize different regimes of cluster diffusion beyond equilibrium.
- To analyze the time dependence of the mean square displacement (MSD) in these regimes.
Main Methods:
- Theoretical investigation of 2D cluster diffusion.
- Analysis of mean square displacement (MSD) under various nonequilibrium scenarios.
- Comparison of theoretical predictions with kinetic Monte Carlo simulations.
Main Results:
- Identified three distinct nonequilibrium diffusion regimes for 2D clusters.
- Curvature-driven evaporation exhibits a square-root singularity in MSD near collapse.
- Slow growth/evaporation follows Edwards-Wilkinson universality (logarithmic MSD).
- Far-from-equilibrium dynamics adhere to Kardar-Parisi-Zhang universality (power-law MSD with exponent 1/3).
Conclusions:
- Nonequilibrium conditions lead to significant deviations in cluster diffusion from equilibrium behavior.
- The identified regimes and their associated MSD behaviors provide a framework for understanding complex cluster dynamics.
- Findings are consistent with simulations and applicable to other universality classes.
Related Concept Videos
02:39Phase Transitions: Vaporization and Condensation
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
01:15Theories of Dissolution: Diffusion Layer Model
Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
01:25Crystal Growth: Principles of Crystallization
Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent – the...
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent – the...
02:20Dynamic Equilibrium
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
01:12Diffusion
Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
01:21Diffusion
Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...