Phase separation of two-component systems in thin films

Katarzyna Bucior, Leonid Yelash, Kurt Binder

Institute of Physics Condensed Matter Theory Group KOMET 331

Johannes-Gutenberg University of Mainz, Germany

Motivation and goals

■ industrial significance of polymer solutions

■ knowledge of the phase behavior

■ influence of confinement on phase separation

[1] B. Krause et al. Macromolecules 2002, 35, 1738

foamed polysulfone film [1] bulk MD simulations thin film MD simulations

MODEL OF A MIXTURE:coarse graining of C16H34 and CO2 molecules

C16H34- represented by flexible chain of 5 segments

(each contains roughly 3 C-C bonds)

CO2- coarse grained into a sphere

726.0,816.0

1,1

22

16384127

4

6offcut

612

LJ

cccc

hhhh

r

rrrU

• bead-spring model for chain molecule FENE+LJ potential [1,2]• LJ potential for CO2-CO2 and non-bonded chain monomers interactions

2

FENE 5.11ln75.33)(

hh

rrU

[1] K. Kremer, G. S. Grest, JCP, 92, 5057 (1990)

[2] L.G. MacDowell, P. Virnau, M. Müller, K. Binder, JCP, 117, 6360 (2002)

type III

type I

TcCO2

TcC16H34

886.0,2/, cchhcchhhc

• cross-interactions between CO2 and C16H34 by LJ potential with hc and hc using Lorentz-Berthelot mixing rule:

bulk phase diagram for C16H34/CO2 mixture [3]

[3] K.Binder, M.Müller, P.Virnau, L.G. MacDowell, Adv. Polym.Sci, 176, 1 (2004)

• two infinite parallel walls consisting of spherical particles

• interactions between fluid particles and wall particles:

6offcut

612

LJ

2

4

r

rrrU U

r

rcut

Confinement:

isothermal slice through the phase diagram of C16H34/CO2

at T=486K [1]

[1] K.Binder, M.Müller, P.Virnau, L.G. MacDowell, Adv. Polym.Sci, 176, 1 (2004)[2] L.G. MacDowell, P.Virnau, M.Müller, K.Binder, JCP, 117, 6360 (2002)

Grand canonical MC TPT1-MSA EOS [2] spinodal curve [2]

molar fraction of CO2

pres

sure

, bar

spinodal decomposition

simulation of phase separation in thin film geometry:

•homogeneous sample in one-phase region of phase diagram (*=0.8, xCO2=0.6, T*=1.16)

system size:Lx=Ly=240, Lz=12

•pressure jump to two-phase region of phase diagram (density decrease to *0.4)

system size: Lx=Ly=300, Lz=15

METHOD

MD simulations with use of ESPResSo [1] parallelized simulation package

1) Preparation of homogeneous sample velocity Verlet algorithm with time step =0.002t with time scale t=(m/)1/2

creating configuration with walls using SAW, box Lx=Ly=20 , Lz=12

NVT warming up (T*=1.16) with Langevin thermostat

switch off thermostat and stop CoM NVE MD

replicate the box in x and y directions (Lx=Ly=20 240 , N=589 999)

relax the periodic structure due to p.b.c.

• Pressure jump

by 25% rescaling of positions of molecules in 3 directions (final system size: Lx=Ly=300, Lz=15)

• Simulation of the system in NVE ensemble (multiprocessor SOFTCOMP, JUMP in Jülich)

[1] www.espresso.mpg.de

time evolution of structure formation

t=100 t=500 t=2000

t=100-3800t=100

t=0

Lx=300 (135nm)

Lz=

15

Lx=300 (135nm)

Ly=3

00

(135

nm)

t=0-500, t=10

DENSITY PROFILES IN Z DIRECTION

CO2C16H34

t

1),0(

1),(),(

tg

trgtrG

scaled real-space correlation function G(r,t):

g(r,t)- pair correlation function

time dependence of characteristic length scale

CONCLUSIONS

•Efficient coarse grained model of a real asymmetric mixture

•Molecular dynamics simulation of pressure jump with use of ESPResSo

•Bicontinuous structure during the spinodal decomposition in quasi 2d

•Characteristic length scales as l~t1/3 (bulk: l~t1/3 to l~t)

ESPResSo: Research group of C. Holm, Max Planck Institute for Polymer Research in Mainz, GermanyCPU time in JUMP cluster and SOFTCOMP in Jülich

Thank you for your attention!Thank you for your attention!

Acknowledgements

•Dr. Peter Virnau (Mainz)•Dr. Subir Das (Mainz)•Dr. Torsten Stühn (MPI Mainz)

http://www.humboldthttp://www.humboldt--foundation.defoundation.de

The speaker’s attendance

at this conference was sponsored

by the

Alexander von Humboldt Foundation.

The speaker’s attendance

at this conference was sponsored

by the

Alexander von Humboldt Foundation.

DENSITY-DENSITY STRUCTURE FACTOR Snn

qSqSqSqS ABBBAAnn 2

BA,,,5.0

,1

exp1 1

f

rqiN

fqS

N

k

N

lkl

partial structure factors:number density structure factor:

homogeneous system before quench system after pressure quench at t=50

LJ peak spinodal

decomposition peak

time dependence of structure factor

3rd layer at z=3.75

5th layer at z=6.75

characteristic domain size R:

cut

cut

qq

qnn

qq

qnn

tqqS

tqS

tR

0

0

),(

),(

2)(

t=10 t=50 t=100 t=200

3rd layer at z=3.75

5th layer at z=6.75

pressure jump: p*=0.21 to p

RELATIVE CONCENTRATION DENSITY PROFILE

)()(

)(

34162

2

zz

z

HCCO

CO

TOTAL DENSITY PROFILE