Dynamics of finite 3D dust clouds beyond the crystalline state Andr - - PowerPoint PPT Presentation

Dynamics of finite 3D dust clouds beyond the crystalline state

• M. Mulsow, A. Melzer, IfP *University of Greifswald,
• P. Ludwig, H. Kählert , M. Bonitz, ITAP Kiel
• J. Schablinski, D. Block, A. Piel, IEAP Kiel

André Schella*

schella@physik.uni-greifswald.de Summer Institute “Complex Plasmas“ South Orange, NJ, August2014

Dusty Plasmas

Summer Institute "Complex Plasmas", South Orange, NJ 2

Greifswald, 6th July 2014 56°6‘N, 12° 23‘ O Selwyn et. al, JVacSciTech 7 (1989) newswatch.nationalgeographic.com

„Dusty Plasma = solid particles + plasma“

Dusty Plasmas (in the Lab)

Morfill et al., PRL 83 (1999) Schmidt et al., Phys Plasmas 18 (2011) Killer et al., Phys. Plasmas 20 (2013)

Monodisperse microspheres

• Diameter: a ≈ µm; charge: Q ≈ 104e

but low Q/m  “slow” dynamics ≈ ms…s

• Large interparticle spacing: b ≈ 500µm

 high transparency

• Low frictional damping

 high dynamics  Trace particles on kinetic level!

2 2 2

10 1 4    T k b e Z

B



Extended dust clouds Finite dust clouds Strongly coupled systems:

1  

D

b  

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N > 105 N < 100 Screening:

Experiment

Arp et al., PRL 93 (2004) Käding2008

Summer Institute "Complex Plasmas", South Orange, NJ

• rf discharge in argon at 13.56 MHz
• dust particles:

4.86 (4.04) micron

• rf power:

1,…,5 W

• pressure:

4,…,8 Pa

• camera :

0.1kfps (1kfps) 30000 (2200) frames

• manipulation lasers:
• max. 1W per laser

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Confinement of 3D Dust Clouds

Arp et al., PRL 93 (2004), Phys. Plasmas 12 (2005) Käding et al., Phys. Plasmas 15 (2008)

 

 

  

N i N j i ij ij i

r r r N E

1 2

) exp( ) , (  

Summer Institute "Complex Plasmas", South Orange, NJ

 

 

  

N i N j i ij D ij i

r r e Z r m E

1 2 2 2 2

) exp( 4 2 1   

Dimensionless Hamiltonian:

Yukawa ball

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Structural aspects of Yukawa Balls

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Arp et al., PRL 93 (2004) Block et al. ,PPCF 49 (2007) Bonitz et al., PRL 96 (2006) Käding et al., Phys. Plasmas 15 (2008 ) Kählert et al., PRE 78 (2008)

• Particle arrangment on nested shells;

surface with defects

• Higher population of inner shells and

parabolically decaying density profile

• High fraction of metastable states

Summer Institute "Complex Plasmas", South Orange, NJ

Schella et al., PRE 84 (2011) Thomsen et al., accepted in JPhysD, Schella et al., PRE 87 (2013) Schella et al., New J. Phys. 15 (2013) Kählert et al., PRE 82 (2010); PRE 83 (2011) Schella et al., Phys. Plasmas 21 (2014) Schella et al., accepted in IEEE

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Beyond the Crystalline State

Outline

• Finite Dust Clouds
• Melting
• Fluid Dynamics
• Diffusive Transport
• Configurational Entropy
• Recrystallization
• Summary

Schella et al., PRE 84 (2011)

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Laser Heating

Schablinski et al., Phys. Plasmas 19 (2012) Thomsen et al., Phys. Plasmas 19 (2012) Schella et al., New J. Phys. 15 (2013)

T k b e Z

B

1 4

2 2

  

 Phase transitions  Fluid arrangements

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Melting by Laser Heating

Schella et al., PRE 84 (2011) Melzer et al., CPP 52 (2012)

N = 53; P = 2.4W; p = 7.5Pa 0 mW 90 mW 400 mW

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Triple Correlation Function (TCF)

TCF: Captures radial order and angular order simultaneously

1 2 1 3 2

1 1

) , , ( ) , ( dr r r g r g

R r

 

  

Thomsen, ITAP, Kiel, 2011 Thomsen, ITAP, Kiel, 2011 Ludwig et al. PPCF 52 (2010)

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Melting by Laser Heating

N = 53; P = 2.4W; p = 7.5Pa

Schella et al., PRE 84 (2011) Melzer et al., CPP 52 (2012)

0 mW 90 mW 400 mW

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Laser Heating: Correlations

Bedanov et al., PRB 49 (1994) Schella et al., PRE 84 (2011) Melzer et al.; CPP 52 (2012)

2-step process: 1. loss of angular order

• 2. loss of radial order

Angular order Radial order

Increasing laser power

1. 2.

N = 53; P = 2.4W; p = 7.5Pa

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Outline

• Finite Dust Clouds
• Melting
• Fluid Dynamics
• Diffusive Transport
• Configurational Entropy
• Recrystallization
• Summary

Schella et al., PRE 87 (2013)

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Motivation

(1,6,12)

Transport/ Unstable Modes Entropy/ Rearrangement

Thermodynamic properties

(1,7,11)

Long time series Short time dynamics

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Motivation

[1] LaNave et al., PRL 84 (2000) [2] Keyes, PRE 62 (2000)

(1,6,12)

Transport/ Unstable Modes Entropy/ Rearrangement

Thermodynamic properties

 

u C

f b a S ln  

(1,7,11)

Long time series Short time dynamics

• Derived for 3D Lennard-Jones (LJ) Fluids, 1 ≤ b ≤ 2 [1,2]

 Valid for finite systems?

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Instantaneous Normal Modes

Keyes, J Chem. Phys. 101 (1994) Stratt, Acc. Chem. 28 (1995) Melzer et al., PRL 108 (2012) Melzer et al., PRE 89 (2014)



 real



 imaginary

Dynamical matrix:

) ( ) ( ) (      

u s

 

Density of states: Eigenvectors and eigenfrequencies at each timestep t:

) (

, t

e l

i

 ) (t

l



Stable modes (real ω): solid properties Unstable modes (imag. ω) : liquid properties

 ) (t H

 



 

l l

     ) (

 

) ( , , 2

,

t r j i r

r t r E





  

 

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INM of Finite 3D Dust Clouds

[1] Keyes, J Chem Phys 101 (1994)

• Large fraction of unstable modes fu (16% - 23%) in 3D,

like LJ Fluids[1]. Heating

   d f

u u





 ) (

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Fraction of unstable modes:

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Diffusion Constant

Melzer et al., PRL 108 (2012)

• Diffusion in 2D more size dependent;

in 3D higher

• Freezing temperature from D(T)  0

TM

 



 

2 2

1     

h h B

d m T k D

3D

      

         d c

s u h







2

1

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2D

TM

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Configurational Entropy

k k k C

p p S



  ln

Textbook Definition: Measure entropy directly from experiment!

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Configurational Melting

• In 2D: Threshold behavior indicates configurational melting
• In 3D: Saturated regime; clusters at elevated temperatures

TM 2D 3D

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Connection to unstable modes?!

From Transport to Disorder

 

u C

f b a S ln  

• Correlation found for 2D clusters

2D 3D From INM From cluster states Configurational entropy Fraction of unstable modes

LaNave et al., PRL 84 (2000) [1] Keyes, PRE 62 (2000)

Summer Institute "Complex Plasmas", South Orange, NJ

Prediction [1]: 1 ≤ b ≤ 2 Experiment (2D): b = 1.7

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Outline

• Finite Dust Clouds
• Melting
• Fluid Dynamics
• Diffusive Transport
• Configurational Entropy
• Recrystallization
• Summary

Summer Institute "Complex Plasmas", South Orange, NJ

Schella et al., accepted in IEEE

23

Recrystallization Experiment

Summer Institute "Complex Plasmas", South Orange, NJ

sedimentation into crystalline structure fluid state while laser heated

) ( 1 4 ) (

2 2

t T k b e Z t

B

  

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Laser ≈1s t heating recrystallization

N = 36; P = 3.8W; p = 8Pa, ten runs N = 19; P = 4.1W; p = 8Pa, eight runs

Coulomb Coupling Parameter

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) exp( ) ( t t

rc

   

• Extended 2D dust crystals[1] : τrc ≈ ν

(ν = friction coefficient, here ν = 21s-1 and ν/ω0 ≈ 1)

• Slow cooling rate comparable to simulations[2]

[1] Knapek et al., PRL 98 (2007) [2] Kählert et al., PRL 104 (2010)

N τrc /ν 36 0.25 ± 0.06 19 0.25 ± 0.11

Initial phase of recrystallization[1]: Cooling rate

Schella et al., Phys. Plasmas 21 (2014)

Correlation Buildup

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 Fit nearest neighbor peak g1 to inverted parabola Less correlated during heating Correlations emerge during recrystallisation

 

) ( ) , ( t r r t r g

ij

    

t = 2s Pair-correlation function:

Time scale of Correlation Buildup

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 Correlation buildup on slower scales than cooling

N τrc /ν (cooling) τcorr /ν (correlation) 36 0.25 ± 0.06 0.19 ± 0.12 19 0.25 ± 0.11 0.14 ± 0.04

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height of g1 (arb. units)

Summary

Melting:

• Correlation loss: two-step process,

captured by TCF

Fluid Dynamics:

• Transport and entropy: Size and temperature effects
• 2D dust clusters: Correlation between transport and

disorder

Schella et al., PRE 87 (2013) Schella et al., PRE 84 (2011)

Summer Institute "Complex Plasmas", South Orange, NJ

Recrystallization:

• Cooling and correlation buildup on slower

scales than neutral gas damping rate

Schella et al., Phys. Plasmas 21 (2014)

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