When is a conductor not perfect? Sum rules fail under critical fluctuations

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Chemistry

Background:

• Conductors exhibit perfect charge screening, a phenomenon theoretically described by the Stillinger-Lovett sum rule.
• The rule relates the charge-charge correlation structure factor, S(ZZ)(k), to the Debye length, temperature, and ion density.

Purpose of the Study:

• To computationally verify the Stillinger-Lovett sum rule in a charge-symmetric hard-sphere electrolyte.
• To investigate the behavior of the structure factor at the critical point (T(c), ρ(c)).

Main Methods:

• Employed grand canonical simulations with a novel finite-size scaling technique.
• Analyzed the charge-charge correlation structure factor, S(ZZ)(k), as a function of momentum transfer (k).

Main Results:

• Confirmed the Stillinger-Lovett sum rule for electrolytes under normal conditions.
• Observed a failure of the Stillinger-Lovett rule at the critical point, contradicting existing theories.
• The k(4) term in the S(ZZ)(k) expansion was found to diverge at criticality, mirroring the behavior of compressibility.

Conclusions:

• The Stillinger-Lovett sum rule is robust for electrolytes but exhibits critical failure.
• This finding necessitates a re-evaluation of charge screening theories at phase transitions.
• The diverging k(4) term provides a new signature for critical phenomena in electrolytes.