February 2015
Spotlight Summary by Brad Deutsch
Testing the Maxwell-Boltzmann distribution using Brownian particles
Since the 1970's, optical tweezers have allowed us to manipulate tiny particles with focused laser beams. The electric field of such a beam "pulls" the particle toward its brightest point near the center. Since then, scientists have been building on this technique, and are now able to trap a particle while simultaneously measuring its position to a precision of less than a nanometer. In this paper, Mo et al. observe single particles as they move inside an optical trap in liquid, recording their trajectories in time steps of a 200 millionth of a second. They use the data to show that the motion can be described by a modification of the theory used for particles in air.
At equilibrium, particles inside a gas of a certain temperature move around with different velocities, which are described by the Maxwell-Boltzmann distribution (MBD). This equation takes the temperature of the solution and the mass of the particles as inputs, and tells us the probability of finding a particle moving at a particular speed. It can be derived from a few basic assumptions about a system: that energy is conserved, that particles follow Newtonian physics, and that the average distance between them is large compared to their sizes. The accuracy of the MBD has been confirmed by experiments in which particles were optically trapped and observed in air.
Here, the authors propose a complication. If the particles are instead in liquid, it should be harder to move them around. The liquid should give them extra inertia, making them seem heavier. They use a laser to trap single particles in various liquids for a second at a time, and closely keep track of its motion on timescales of tens of nanoseconds. The particle casts a shadow in the laser beam, and by looking at the symmetry of the shadow, the team can determine the particle's position. The change in position from one instant in time to the next tells them the velocity, and by tallying up all of the velocities they can create a distribution to compare to theory.
The measured distribution doesn't match the MBD for a particle in air, but replacing the particle's mass with a modified or "effective" mass causes the theory to be in line with the experimental results. The authors point out that this type of measurement could be used in other kinds of exotic fluids, where more extreme modifications from the MBD should be necessary.
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At equilibrium, particles inside a gas of a certain temperature move around with different velocities, which are described by the Maxwell-Boltzmann distribution (MBD). This equation takes the temperature of the solution and the mass of the particles as inputs, and tells us the probability of finding a particle moving at a particular speed. It can be derived from a few basic assumptions about a system: that energy is conserved, that particles follow Newtonian physics, and that the average distance between them is large compared to their sizes. The accuracy of the MBD has been confirmed by experiments in which particles were optically trapped and observed in air.
Here, the authors propose a complication. If the particles are instead in liquid, it should be harder to move them around. The liquid should give them extra inertia, making them seem heavier. They use a laser to trap single particles in various liquids for a second at a time, and closely keep track of its motion on timescales of tens of nanoseconds. The particle casts a shadow in the laser beam, and by looking at the symmetry of the shadow, the team can determine the particle's position. The change in position from one instant in time to the next tells them the velocity, and by tallying up all of the velocities they can create a distribution to compare to theory.
The measured distribution doesn't match the MBD for a particle in air, but replacing the particle's mass with a modified or "effective" mass causes the theory to be in line with the experimental results. The authors point out that this type of measurement could be used in other kinds of exotic fluids, where more extreme modifications from the MBD should be necessary.
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Article Information
Testing the Maxwell-Boltzmann distribution using Brownian particles
Jianyong Mo, Akarsh Simha, Simon Kheifets, and Mark G. Raizen
Opt. Express 23(2) 1888-1893 (2015) View: Abstract | HTML | PDF