How to Compute Density Fluctuations at the Nanoscale.

Area of Science:

• Statistical Mechanics
• Physical Chemistry
• Condensed Matter Physics

Background:

• Standard particle number fluctuations overlook excluded volume effects.
• This leads to systematic finite-size scaling errors and unphysical surface terms in isothermal compressibility.
• Existing models fail to accurately represent density fluctuations in small volumes.

Purpose of the Study:

• To correct errors in standard particle number fluctuation theory.
• To introduce a modified pair distribution function accounting for finite particle size.
• To enable accurate computation of local compressibility at the nanometer scale.

Main Methods:

• Developed a modified pair distribution function incorporating excluded volume effects.
• Applied the new theory to a one-dimensional hard sphere fluid.
• Calculated number fluctuations using the modified theory.

Main Results:

• The modified theory eliminates systematic finite-size scaling errors.
• Demonstrated size-independent compressibility for a one-dimensional hard sphere fluid.
• Achieved accurate density fluctuation calculations in sub-particle-sized volumes.

Conclusions:

• The new theory accurately captures particle number fluctuations by including excluded volume effects.
• This approach resolves unphysical surface terms in isothermal compressibility.
• Paves the way for nanoscale local compressibility measurements using fluctuation theory.