Canonical free-energy barrier of particle and polymer cluster formation

Abstract

A common approach to study nucleation rates is the estimation of free-energy barriers. This usually requires knowledge about the shape of the forming droplet, a task that becomes notoriously difficult in macromolecular setups starting with a proper definition of the cluster boundary. Here, we demonstrate a shape-free determination of the free energy for temperature-driven cluster formation in particle as well as polymer systems. Combined with rigorous results on equilibrium droplet formation, this allows for a well-defined finite-size scaling analysis of the effective interfacial free energy at fixed density. We first verify the theoretical predictions for the formation of a liquid droplet in a supersaturated particle gas by generalized-ensemble Monte Carlo simulations of a Lennard-Jones system. Going one step further, we then generalize this approach to cluster formation in a dilute polymer solution. Our results suggest an analogy with particle condensation, when the macromolecules are interpreted as extended particles.

arXiv comment10 pages, 4 figures

References in corpus (23)

• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Phase changes in 38 atom Lennard-Jones clusters. II: A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical
• Inconsistent thermostatistics and negative absolute temperatures
• Entropic Effect on the Rate of Dislocation Nucleation
• Systematic Improvement of Classical Nucleation Theory
• Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems
• On the formation/dissolution of equilibrium droplets
• Scaling Properties of a Parallel Implementation of the Multicanonical Algorithm
• Finite size effects on liquid-solid phase coexistence and the estimation of crystal nucleation barriers
• Microcanonical Approach to the Simulation of First-Order Phase Transitions
• Overcoming timescale and finite-size limitations to compute nucleation rates from small scale Well Tempered Metadynamics simulations
• Phase transition to bundles of flexible supramolecular polymers
• Critical region for droplet formation in the two-dimensional Ising model
• The Gibbs "volume" entropy is incorrect
• Shape and area fluctuation effects on nucleation theory
• From amorphous aggregates to polymer bundles: The role of stiffness on structural phases in polymer aggregation
• Free energy of cluster formation and a new scaling relation for the nucleation rate
• Monte Carlo study of the evaporation/condensation transition on different Ising lattices
• Aggregation of theta-polymers in spherical confinement
• Exploring different regimes in finite-size scaling of the droplet condensation-evaporation transition
• Microcanonical phase diagrams of short-range ferromagnets
• Application of the parallel multicanonical method to lattice gas condensation
• Thermodynamic laws in isolated systems

Cited by in corpus (13)

• Local Structure Order Assisted Two-step Crystal Nucleation in Polyethylene
• Massively parallel multicanonical simulations
• Equivalence between condensation and boiling in a Lennard Jones fluid
• The barrier to ice nucleation in monatomic water
• Free Energy Barriers for Crystal Nucleation from Fluid Phases
• Microcanonical characterization of first-order phase transitions in a generalized model for aggregation
• Shape-free theory for the self-assembly kinetics in macromolecular systems
• Transition barrier at a first-order phase transition in the canonical and microcanonical ensemble
• Kinetics of first-order phase transitions from microcanonical thermostatistics
• Effect of grafting on the binding transition of two flexible polymers
• From particle condensation to polymer aggregation
• The Droplet Formation-Dissolution Transition in Different Ensembles: Finite-Size Scaling from Two Perspectives
• Shape characteristics of the aggregates formed by amphiphilic stars in water: dissipative particle dynamics study