Dynamics of finite 3D dust clouds beyond the crystalline state

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* [email protected]

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

0

22

101

4

Tkb

eZ

B

Extended dust clouds

Finite dust clouds

Strongly coupled systems:

1 Db


3

N > 105

N < 100

Screening:

Experiment

Arp et al., PRL 93 (2004)

Käding2008


• 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

4

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

ji ij

ij

ir

rrNE

1

2)exp(

),(


N

i

N

ji ij

Dij

ir

reZrmE

1 0

2222

0

)exp(

42

1

Dimensionless Hamiltonian:

Yukawa ball

5

Structural aspects of Yukawa Balls


6

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


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

7

Beyond the Crystalline State

Outline

• Finite Dust Clouds

• Melting • Fluid Dynamics

• Diffusive Transport

• Configurational Entropy

• Recrystallization

• Summary Schella et al., PRE 84 (2011)


8

Laser Heating

Schablinski et al., Phys. Plasmas 19 (2012)

Thomsen et al., Phys. Plasmas 19 (2012)

Schella et al., New J. Phys. 15 (2013)

Tkb

eZ

B

1

4 0

22

Phase transitions Fluid arrangements


9

Melting by Laser Heating


Melzer et al., CPP 52 (2012)

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

0 mW 90 mW 400 mW


10

Triple Correlation Function (TCF)

TCF: Captures radial order and angular order simultaneously

1213211

),,(),( drrrgrgRr

Thomsen, ITAP, Kiel, 2011

Thomsen, ITAP, Kiel, 2011

Ludwig et al. PPCF 52 (2010)


11

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


12

Laser Heating: Correlations

Bedanov et al., PRB 49 (1994)


Melzer et al.; CPP 52 (2012)

2-step process: 1. loss of angular order 2. loss of radial order

Angular order Radial order

Incr

easi

ng

lase

r p

ow

er

1.

2.

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


13

Outline


• Melting

• Fluid Dynamics • Diffusive Transport


• Recrystallization

• Summary



14

Motivation (1,6,12)

Transport/ Unstable Modes

Entropy/ Rearrangement

Thermodynamic properties

(1,7,11)

Long time series

Short time dynamics


15

Motivation

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

[2] Keyes, PRE 62 (2000)

(1,6,12)

Transport/ Unstable Modes

Entropy/ Rearrangement

Thermodynamic properties

uC fbaS 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?


16

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:

)()()( us

Density of states:

Eigenvectors and eigenfrequencies at each timestep t:

)(, te li

)(tl

Stable modes (real ω): solid properties

Unstable modes (imag. ω) : liquid properties

)(tH

l

l )(

)(,,

2 ,

trji rr

trE


17

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

df uu

0

)(


Fraction of unstable modes:

18

Diffusion Constant

Melzer et al., PRL 108 (2012)

• Diffusion in 2D more size dependent; in 3D higher

• Freezing temperature from D(T) 0

TM

221

h

hB dm

TkD

3D

dc

s

uh

2

1


2D

TM

19

Configurational Entropy

k

k

kC ppS ln

Textbook Definition:

Measure entropy directly from experiment!


20

Configurational Melting

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

TM

2D

3D


21

Connection to unstable modes?!

From Transport to Disorder

uC fbaS 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)


Prediction [1]: 1 ≤ b ≤ 2

Experiment (2D): b = 1.7

22

Outline


• Melting

• Fluid Dynamics • Diffusive Transport


• Recrystallization • Summary


Schella et al., accepted in IEEE

23

Recrystallization Experiment


sedimentation into crystalline structure

fluid state while laser heated

)(

1

4)(

0

22

tTkb

eZt

B

24

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


25

)exp()( 0 tt 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


Correlation Buildup


26

Fit nearest neighbor peak g1 to inverted parabola

Less correlated during heating

Correlations emerge during recrystallisation

)(),( trrtrg ij

t = 2s

Pair-correlation function:

Time scale of Correlation Buildup


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

27

hei

ght

of

g 1 (

arb

. un

its)

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




Recrystallization: • Cooling and correlation buildup on slower

scales than neutral gas damping rate


28

Documents

Dynamics of finite 3D dust clouds beyond the crystalline state