Hartmut-Loewen.pdf

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Outline: 1) DDensity it ffunctional ti l theory th of f freezing: f i spheres h 1.1 Phenomenological results 11.2 2 Independent treatment of the different phases 1.3 Unifying Microscopic theories 1.4 Phase diagrams of simple potentials 1.5 Density Functional Theory (DFT) 2) Brownian Dynamics and dynamical density functional theory 2.1 Brownian dynamics (BD) 2.2 Dynamical density functional theory (DDFT) 2.3 Hydrodynamic interactions 3) ) Density y functional theory yfor rod-like particles p 3.1 Statistical mechanics of rod-like particles 3.2 Simple models 3.3 Brownian dynamics of rod-like particles
1) Density functional theory of freezing: spheres 1.1) Phenomenological results: experiments: - liquids crystallize into periodic structures at low temperatures or/and high densities - translational symmetry is broken - one of fth the most ti important t tphase h ttransitions iti iin nature t - when does it happen?
Page 1: 3rd Warsaw School of Statictical Ph
Page 5 and 6: ii) Hansen-Verlet rule of freezing
Page 7 and 8: Maxwell-double tangent construction
Page 9 and 10: 1.4) Phase diagrams of simple poten
Page 11 and 12: ) plasma (with neutralizing backgro
Page 13 and 14: e) Lennard-Jones-system phase p dia
Page 15 and 16: g) ultrasoft interactions repulsive
Page 17 and 18: exceptions: i) ) soft potentials p
Page 19 and 20: contour plot of
Page 21 and 22: approximations on different levels
Page 23 and 24: 3) Ramakrishnan-Youssuf (RY) 1979 i
Page 25 and 26: 5) Rosenfeld functional (for hard s
Page 27 and 28: advantages - excludes overlapping h
Page 29 and 30: 2) Brownian Dynamics and dynamical
Page 31 and 32: Thi This is i valid lid for f ffree
Page 33 and 34: Smoluchowski equation Diffusion in
Page 35 and 36: linear relation between and One can
Page 37 and 38: Langevin-picture Smoluchowski-pictu
Page 39 and 40: with hydrodynamic interactions(HI.)
Page 41 and 42: integration yields 2-particle densi
Page 44 and 45: 3) in equilibrium, necessarily
Page 46 and 47: in equilibrium, DFT says: apply com
Page 48 and 49: colloidal particles colloidal dispe
Page 50 and 51: The road map of complexity H. Löwe
Page 52 and 53:
particle p configurations g for dif
Page 54 and 55:
DDFT, , equilibrium q functional by
Page 56 and 57:
imposed nucleation seed cut-out of
Page 58 and 59:
no nucleation 0 φ= 60 Aρ = 0.6
Page 60 and 61:
Two stage process: - sub-Brownian t
Page 62 and 63:
2.3) Hydrodynamic interactions How
Page 64 and 65:
2) Rotne-Prager-tensor with 3) high
Page 66 and 67:
Rotne-Prager expression ( r ) = 0 v
Page 68 and 69:
Application: colloids in an oscilla
Page 70 and 71:
stroboscopic view t i /t B = 2.5, 2
Page 72 and 73:
3) Density functional theory for ro
Page 74 and 75:
density of center-of-masses: orient
Page 76 and 77:
(2) nematic phase positions iti are
Page 78 and 79:
three eigenvalues with largest eige
Page 80 and 81:
(5) columnar phase: (6) plastic cry
Page 82 and 83:
3.2) Simple models hard objects A)
Page 84 and 85:
C) Density functional theory There
Page 86 and 87:
3.3) Brownian dynamics of rod-like
Page 88 and 89:
“adiabatic“ approximation: assu
Page 90 and 91:
Model Gaussian segment-segment segm
Page 93 and 94:
full density orientationally averag
Page 95 and 96:
σ 3 ρ(z) 10 8 set-up A DDFT (soli
Page 97 and 98:
expansion compression transient par
Page 99 and 100:
mm (t) ( 2 7.5 5 2.5 0 -2.5 -5 m 2
Page 101 and 102:
From „passive“ to „active“
Page 103 and 104:
L. Baraban, private communication m
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