Does the configurational entropy of polydisperse particles exist?

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Materials Science

Background:

• Classical particle systems with continuous size polydispersity present challenges for statistical mechanics due to particle distinguishability and divergent mixing entropy.
• Standard computational methods for glassy states yield divergent configurational entropy in polydisperse systems, seemingly contradicting experimental observations of glass transitions.

Purpose of the Study:

• To resolve the paradox of divergent configurational entropy in continuously polydisperse systems.
• To propose a physically meaningful method for computing finite configurational entropy in such systems.
• To demonstrate the existence and quantifiability of configurational entropy in polydisperse materials.

Main Methods:

• Developed a method based on an effective M*-component system description with finite M*.
• Determined M* directly from computer simulations across various glass-forming models.
• Investigated systems with hard/soft and additive/non-additive interparticle interactions and diverse size polydispersities.

Main Results:

• The proposed method yields finite and physically meaningful mixing and configurational entropies.
• Successfully computed configurational entropy for continuously polydisperse systems.
• Demonstrated the universality of the approach across different interaction potentials and polydispersity levels.

Conclusions:

• The apparent divergence of configurational entropy in polydisperse systems arises from a misinterpretation of phase space configurations versus free energy states.
• Continuously polydisperse systems can and do exhibit a finite configurational entropy.
• The developed computational approach provides a consistent and quantitative means to estimate configurational entropy in these complex materials.