De Gennes Narrowing and Hard-Sphere Approach.

Area of Science:

• Condensed Matter Physics
• Computational Physics
• Liquid State Theory

Background:

• The energy width (Δω) of the quasielastic coherent dynamic structure factor S(Q, ω) in simple liquids shows an oscillating dependence on wavenumber (Q).
• A known expression for Δω(Q) exists for dense hard-sphere (HS) fluids, often applied to liquid metal data, but its validity for true HS fluids was untested.

Purpose of the Study:

• To test the existing hard-sphere (HS) model for the energy width Δω(Q) against molecular dynamics simulations of a true HS fluid.
• To investigate the factors governing Δω(Q) in HS fluids and compare dynamics in HS and soft-sphere systems.
• To explore effective parameters for characterizing soft-sphere fluid dynamics within the HS framework.

Main Methods:

• Molecular dynamics simulations of a hard-sphere (HS) fluid.
• Analysis of the quasielastic coherent dynamic structure factor S(Q, ω) and its energy width Δω(Q).
• Comparison of simulation results with theoretical models and experimental data for liquid metals (e.g., Rb).

Main Results:

• Significant discrepancies were found between the existing HS model and simulation results for Δω(Q).
• The energy width Δω(Q) in HS fluids is primarily determined by the average cage size (⟨Lc⟩), not the HS diameter (σHS).
• Soft-sphere fluid dynamics, while different from HS, can be characterized using an effective diameter (σeff) derived from Δω(Q) at Q ≈ Qmax, consistent with liquid Rb data.

Conclusions:

• The established hard-sphere model for energy width is inadequate for accurately describing true HS fluid dynamics.
• Average cage size is a critical parameter for understanding the energy width in simple liquids.
• An effective diameter approach can bridge the gap between hard-sphere approximations and the dynamics of soft-sphere systems and real liquid metals.