Large and Long-Range Dynamic Correlations in Supercooled Fluids Revealed via Four-Point Correlation Functions

Area of Science:

• Condensed matter physics
• Statistical mechanics

Background:

• Dynamic heterogeneity in supercooled fluids is typically studied using four-point structure factors.
• Existing methods may not fully capture the extent of dynamic correlations.

Purpose of the Study:

• To introduce and analyze an alternative four-point structure factor.
• To investigate its ability to reveal larger and longer-range dynamic correlations.

Main Methods:

• Comparison of two four-point structure factors: S4(F)(q, k; t) and S4(cos)(q, k; t).
• Analysis of the mobility field definitions: full microscopic self-intermediate scattering function versus its real part.
• Examination of susceptibility (χ4) and correlation length (ξ4) for both structure factors.

Main Results:

• The alternative structure factor S4(F)(q, k; t) yields significantly larger susceptibility (χ4(F)) and correlation length (ξ4(F)).
• The correlation length ξ4(F)(τα) exhibits a growth proportional to relaxation time (∼ τα).
• This contrasts with the weaker dependence of ξ4(cos)(τα) on relaxation time.

Conclusions:

• The proposed S4(F)(q, k; t) uncovers substantial dynamic correlations missed by conventional S4(cos)(q, k; t).
• The observed growth in ξ4(F)(τα) is attributed to transient elastic response.
• The standard S4(cos)(q, k; t) primarily captures domains of slow and fast particles characteristic of dynamic heterogeneity.