The Laplace approach in microrheology

Area of Science:

• Materials Science
• Physical Chemistry
• Polymer Science

Background:

• Micro-rheology is increasingly used to probe material dynamics.
• The generalized Stokes-Einstein (GSE) equation is commonly applied to micro-rheology data.
• Discrepancies between micro- and macroscopic rheology are often reported, particularly in condensed systems.

Purpose of the Study:

• To empirically compare different methods of extracting dynamic moduli from micro-rheology mean-square displacement (MSD) data.
• To assess the agreement between micro-rheological results and macroscopic rheological measurements.
• To provide recommendations for interpreting micro-rheology MSD data.

Main Methods:

• Calculation of dynamic moduli (G' and G'') from MSD using analytical continuation of the Fourier transform.
• Calculation of viscoelastic functions (relaxation modulus or creep compliance) from MSD using direct inverse Laplace transform.
• Comparison of results obtained from Fourier and direct inverse Laplace transform methods.
• Comparison of micro-rheology results with macroscopic rheological measurements.

Main Results:

• The direct inverse Laplace transform approaches can yield different results compared to the Fourier transform approach.
• Direct inverse Laplace transform methods show better agreement with macroscopic rheological measurements in certain cases.
• Instances of agreement between the Fourier transform and direct inverse Laplace transform approaches were also observed.

Conclusions:

• The choice of data analysis method for micro-rheology MSD is critical.
• Direct inverse Laplace transform methods are recommended for interpreting micro-rheology MSD data for improved agreement with macroscopic rheology.
• Further investigation into the nuances of GSE equation application in micro-rheology is warranted.