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Communication: translational Brownian motion for particles of arbitrary shape
Bogdan Cichocki1, Maria L Ekiel-Jeżewska, Eligiusz Wajnryb
1Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland.
The Journal of Chemical Physics
|February 25, 2012
Summary
The long-time slope of a Brownian particle's mean square displacement is independent of reference point choice. This slope is uniquely determined by the mobility matrix trace, crucial for dynamic light scattering.
Area of Science:
- Physics
- Physical Chemistry
- Statistical Mechanics
Background:
- Brownian motion describes random particle movement due to molecular collisions.
- Understanding particle displacement is key in fields like colloid science and biophysics.
- The Smoluchowski equation models the evolution of particle position probability.
Purpose of the Study:
- To analyze the time-dependent translational mean square displacement (W(t)) of an arbitrary-shaped Brownian particle.
- To determine if the long-time behavior of W(t) depends on the chosen reference point.
- To establish a connection between W(t) and fundamental particle properties like the mobility matrix.
Main Methods:
- Solving the Smoluchowski equation for a single Brownian particle.
- Analyzing the time evolution of the mean square displacement W(t).
- Investigating the long-time limit behavior of W(t) and its relation to rotational relaxation times.
Main Results:
- The slope of W(t) becomes independent of the reference point at times exceeding the rotational Brownian relaxation timescale.
- In the long-time limit, the slope of W(t) is uniquely determined by the trace of the translational-translational mobility matrix.
- This trace is evaluated with respect to the hydrodynamic center of mobility.
Conclusions:
- The long-time translational dynamics of arbitrary-shaped Brownian particles are robust and independent of arbitrary reference point selection.
- The derived relationship provides a direct link between measurable quantities in dynamic light scattering and fundamental hydrodynamic properties.
- This finding simplifies the interpretation of experimental data in dynamic light scattering and related fields.
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