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Phonon Spectrum Analysis in a 1D Yukawa Chain of Colloidal Microspheres

This study investigates the phonon spectrum of a one-dimensional Yukawa chain formed by polymer microspheres trapped in a dusty plasma. We experimentally observed the lowest-order sloshing and breathing modes and analyzed the elastic vibrations through video microscopy. Our method includes measuring the particle motion and calculating the current correlation function to derive the dispersion relation of the phonons. The experimental setup utilizes laser manipulation to excite vibrational modes in the microspheres, elucidating the unique characteristics of these soft colloidal structures under low-density plasma conditions.

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Phonon Spectrum Analysis in a 1D Yukawa Chain of Colloidal Microspheres

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  1. Phonon spectrum measured in a 1D Yukawa chain John Goree & Bin Liu

  2. Modes in 1-D chains • Colloids: • Polymer microspheres trapped by counter-propagating laser beams • Lowest-order modes (sloshing & breathing modes) observed experimentally • Carbon nanotubes: • Xe atoms trapped on a tube • Theory: phonon spectrum Tatarkova, et al., PRL 2002 Cvitas and Siber, PRB 2003

  3. Modes in a 1-D chain Longitudinal mode • Transverse mode

  4. Experimental system: dusty plasma • Like a colloidal suspension: • polymer microspheres • electrically charged • suspended in medium that provides screening • colloidal crystals • optical methods include: • direct imaging of particles • laser manipulation

  5. Experimental system: dusty plasma • The medium is a plasma: • a low-pressure gas • partially ionized by applying high voltage

  6. Experimental system: dusty plasma What’s special about plasma: • Medium is low density: • gas instead of a solvent • microspheres are underdamped • Suspension is very soft: • shear modulus of a 3D crystal is ´1019 smaller,as compared to metals • Temperature can be varied: • not in this talk

  7. Microspheres • Melamine formaldehyde • diameter 8.09 mm • introduced into plasma by shaking a dispenser

  8. In this experiment: • charge Q - 7600 e • screeninglength lD 0.86 mm • spacing a 0.80 mm } >> particle radius 4 mm Pair potential Particles suspended as a monolayer interact with a repulsive Yukawa potential:

  9. Suspension of Microspheres • Microspheres: • have no buoyancy • levitated by electric field a few mm above electrode substrate • form horizontal monolayer • no out-of-plane buckling is observed • ordered lattice QE mg electrode substrate

  10. Setup: Ar laser beam 1

  11. Making a one-dimensional chain

  12. Microspheres are trapped above the groove resonant frequency 0.1 Hz 3 Hz groove 15 Hz “Channel” on substrate to confine a chain Groove-shaped channel in lower electrode shapes the E field that confines particles

  13. particle’s x,y position measured in each video frame Image of chain in experiment

  14. incident laser beam momentum imparted to microsphere Vibrational Excitation • Elastic vibrations can be excited by: • Brownian motion in gas • Laser manipulation

  15. 1 mm Experiment:Natural motion of a 1-D chain (no manipulation) central portion of a 28-particle chain

  16. Measuring phonon spectrum • Method: • Video microscopy • Particle tracking Þx(t) & v(t): • Calculate current correlation function C(q,t) • Fourier transform ÞC(q,w)

  17. Phonon spectrum Color corresponds to energy Energy is concentrated in a band that corresponds to a dispersion relation Symbols indicate peaks

  18. Phonon spectrum Color corresponds to energy Energy is concentrated in a band that corresponds to a dispersion relation Symbols indicate peaks

  19. modulated beam 1 mm -I0 ( 1 + sint ) continuous beam I0 Excitation with laser manipulation Net force µI0 sint Wave propagates to two ends of chain

  20. longitudinal transverse N = 28 N = 28 ○ excited Ñ natural ○ excited Ñ natural Dispersion relation - natural & externally excited

  21. Summary • We used direct imaging to observe particle motion in a 1-D chain • We characterized the phonons by: • Power spectra • Dispersion relation • More details & theory: • Liu, Avinash & Goree PRL 2003 • Liu & Goree PRE 2005

  22. Images of one-dimensional chains

  23. Modulating the laser power scanning mirror Ar laser beam

  24. Argon laser beam Argon laser beam Experiment result • wave: • is excited in the middle of chain • propagates to two ends of chain

  25. Thermal motion Gas temperature = room temperature Particle kinetic temperature was computed from particle velocities 230 K from mean kinetic energy: 390K from fit of velocity distribution function:

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