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

Dynamics of finite 3D dust clouds beyond the crystalline state André Schella* schella@physik.uni-greifswald.de Summer Institute “Complex Plasmas“ South Orange, NJ, August2014 M. Mulsow, A. Melzer, IfP *University of Greifswald, P. Ludwig, H. Kählert , M. Bonitz, ITAP Kiel J. Schablinski, D. Block, A. Piel, IEAP Kiel

Dusty Plasmas Greifswald, 6th July 2014 56 °6‘N, 12° 23‘ O „ Dusty Plasma = solid particles + plasma “ newswatch.nationalgeographic.com Selwyn et. al, JVacSciTech 7 (1989) Summer Institute "Complex Plasmas", 2 South Orange, NJ

Dusty Plasmas (in the Lab) Monodisperse microspheres Extended dust clouds • Diameter: a ≈ µm; charge: Q ≈ 10 4 e but low Q/m  “ slow ” dynamics ≈ ms…s • Large interparticle spacing: b ≈ 500µm N > 10 5  high transparency Morfill et al., PRL 83 (1999) • Low frictional damping Schmidt et al., Phys Plasmas 18 (2011) Killer et al., Phys. Plasmas 20 (2013)  high dynamics N < 100  Trace particles on kinetic level! Strongly coupled systems: Screening: 2 2 Z e 1   b      2 1 10  D 4 b k T 0 B Finite dust clouds Summer Institute "Complex Plasmas", 3 South Orange, NJ

Experiment Arp et al., PRL 93 (2004) Käding2008 • rf discharge in argon at 13.56 MHz • pressure: 4,…,8 Pa • dust particles: 4.86 (4.04) micron • camera : 0.1kfps (1kfps) 30000 (2200) frames • rf power: 1,…,5 W • manipulation lasers: max. 1W per laser Summer Institute "Complex Plasmas", 4 South Orange, NJ

Confinement of 3D Dust Clouds Yukawa ball Arp et al., PRL 93 (2004), Phys. Plasmas 12 (2005) Käding et al., Phys. Plasmas 15 (2008)   2 2 N N exp( r ) 1  Z e     ij D 2 2 E m r  0 i 2 4 r   i 1 i j 0 ij   N N exp( r ) Dimensionless      ij 2 E ( N , ) r Hamiltonian : i r   i 1 i j ij Summer Institute "Complex Plasmas", 5 South Orange, NJ

Structural aspects of Yukawa Balls Block et al. ,PPCF 49 (2007) Arp et al., PRL 93 (2004) Bonitz et al., PRL 96 (2006) • Particle arrangment on nested shells ; surface with defects • Higher population of inner shells and parabolically decaying density profile • High fraction of metastable states Käding et al., Phys. Plasmas 15 (2008 ) Kählert et al., PRE 78 (2008) Summer Institute "Complex Plasmas", 6 South Orange, NJ

Beyond the Crystalline State Schella et al., Phys. Plasmas 21 (2014) Schella et al., accepted in IEEE Schella et al., PRE 84 (2011) Thomsen et al., accepted in JPhysD, Schella et al., New J. Phys. 15 (2013) Schella et al., PRE 87 (2013) Kählert et al., PRE 82 (2010); PRE 83 (2011) Summer Institute "Complex Plasmas", 7 South Orange, NJ

Outline • Finite Dust Clouds • Melting • Fluid Dynamics • Diffusive Transport • Configurational Entropy • Recrystallization • Summary Schella et al., PRE 84 (2011) Summer Institute "Complex Plasmas", 8 South Orange, NJ

Laser Heating 2 2 Z e 1    4 b k T 0 B  Phase transitions  Fluid arrangements Schablinski et al., Phys. Plasmas 19 (2012) Thomsen et al., Phys. Plasmas 19 (2012) Schella et al., New J. Phys. 15 (2013) Summer Institute "Complex Plasmas", 9 South Orange, NJ

Melting by Laser Heating 400 mW 0 mW 90 mW Schella et al., PRE 84 (2011) Melzer et al., CPP 52 (2012) N = 53; P = 2.4W; p = 7.5Pa Summer Institute "Complex Plasmas", 10 South Orange, NJ

Triple Correlation Function (TCF) Thomsen, ITAP, Kiel, 2011 Ludwig et al. PPCF 52 (2010) Thomsen, ITAP, Kiel, 2011      g ( r , ) g ( r , r , ) dr 2 3 1 2 1 r R 1 1 TCF: Captures radial order and angular order simultaneously Summer Institute "Complex Plasmas", 11 South Orange, NJ

Melting by Laser Heating 400 mW 0 mW 90 mW N = 53; P = 2.4W; p = 7.5Pa Schella et al., PRE 84 (2011) Melzer et al., CPP 52 (2012) Summer Institute "Complex Plasmas", 12 South Orange, NJ

Laser Heating: Correlations Angular order Radial order Increasing laser power 2. 1. 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 N = 53; P = 2.4W; p = 7.5Pa 2. loss of radial order Summer Institute "Complex Plasmas", 13 South Orange, NJ

Outline • Finite Dust Clouds • Melting • Fluid Dynamics • Diffusive Transport • Configurational Entropy • Recrystallization Schella et al., PRE 87 (2013) • Summary Summer Institute "Complex Plasmas", 14 South Orange, NJ

Motivation (1,6,12) Thermodynamic properties Transport / Entropy / Unstable Modes Rearrangement Long time Short time series dynamics (1,7,11) Summer Institute "Complex Plasmas", 15 South Orange, NJ

Motivation (1,6,12) Thermodynamic properties Transport / Entropy / Unstable Modes Rearrangement     S a b ln f C u Long time Short time series dynamics (1,7,11) • Derived for 3D Lennard-Jones (LJ) Fluids , 1 ≤ b ≤ 2 [1,2] [1] LaNave et al., PRL 84 (2000)  Valid for finite systems? [2] Keyes, PRE 62 (2000) Summer Institute "Complex Plasmas", 16 South Orange, NJ

Instantaneous Normal Modes     2 E r , t  Dynamical matrix: H ( t )    r i r   , , j r ( t ) Eigenvectors and  eigenfrequencies  e l , t ( ) ( t ) i l at each timestep t :  real            Density of states: ( ) l l         ( ) ( ) ( )  imaginary s u  Stable modes Unstable modes (real ω ): (imag. ω ) : Keyes, J Chem. Phys. 101 (1994) Stratt, Acc. Chem. 28 (1995) solid properties liquid properties Melzer et al., PRL 108 (2012) Melzer et al., PRE 89 (2014) Summer Institute "Complex Plasmas", 17 South Orange, NJ

INM of Finite 3D Dust Clouds Heating Fraction of unstable modes:       f ( ) d u u 0 • Large fraction of unstable modes f u (16% - 23%) in 3D, like LJ Fluids [1] . [1] Keyes, J Chem Phys 101 (1994) Summer Institute "Complex Plasmas", 18 South Orange, NJ

Diffusion Constant 2D 3D T M T M Melzer et al., PRL 108 (2012)  k T       B h D d • Diffusion in 2D more size dependent;    2 2 m 1 in 3D higher   h         • Freezing temperature from D(T)  0       1 u c d    h 2 s Summer Institute "Complex Plasmas", 19 South Orange, NJ

Configurational Entropy Textbook Definition: Measure entropy directly    from experiment! S p ln p C k k k Summer Institute "Complex Plasmas", 20 South Orange, NJ

Configurational Melting 2D 3D T M • In 2D: Threshold behavior indicates configurational melting • In 3D: Saturated regime; clusters at elevated temperatures  Connection to unstable modes?! Summer Institute "Complex Plasmas", 21 South Orange, NJ

From Transport to Disorder From INM Configurational Fraction of entropy unstable modes 3D 2D     S a b ln f C u LaNave et al., PRL 84 (2000) [ 1] Keyes, PRE 62 (2000) Prediction [1] : 1 ≤ b ≤ 2 Experiment (2D): b = 1.7 • Correlation found for 2D clusters From cluster states Summer Institute "Complex Plasmas", 22 South Orange, NJ

Outline • Finite Dust Clouds • Melting • Fluid Dynamics • Diffusive Transport • Configurational Entropy • Recrystallization Schella et al., accepted in IEEE • Summary Summer Institute "Complex Plasmas", 23 South Orange, NJ

Recrystallization Experiment 2 2 Z e 1   ( t )  4 b k T ( t ) 0 B Laser ≈1s t heating recrystallization  fluid state while  sedimentation into laser heated crystalline structure N = 36; P = 3.8W; p = 8Pa, ten runs N = 19; P = 4.1W; p = 8Pa, eight runs Summer Institute "Complex Plasmas", 24 South Orange, NJ

Coulomb Coupling Parameter Initial phase of recrystallization [1] :     ( t ) exp( t ) 0 rc Cooling rate N τ rc / ν 36 0.25 ± 0.06 0.25 ± 0.11 19 Schella et al., Phys. Plasmas 21 (2014) [1] Knapek et al., PRL 98 (2007) [2] Kählert et al., PRL 104 (2010) • Extended 2D dust crystals [1] : τ rc ≈ ν ( ν = friction coefficient, here ν = 21s -1 and ν / ω 0 ≈ 1) • Slow cooling rate comparable to simulations [2] Summer Institute "Complex Plasmas", 25 South Orange, NJ

Correlation Buildup Pair-correlation function:        g ( r , t ) r r ( t ) ij Less correlated during heating Correlations emerge during recrystallisation t = 2s  Fit nearest neighbor peak g 1 to inverted parabola Summer Institute "Complex Plasmas", 26 South Orange, NJ

Time scale of Correlation Buildup height of g 1 (arb. units) N τ rc / ν (cooling) τ corr / ν (correlation) 36 0.25 ± 0.06 0.19 ± 0.12 19 0.25 ± 0.11 0.14 ± 0.04  Correlation buildup on slower scales than cooling Summer Institute "Complex Plasmas", 27 South Orange, NJ