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

foamed polysulfone film [1] thin film MD simulations Motivation and goals industrial significance of polymer solutions knowledge of the phase behavior influence of confinement on phase separation foamed polysulfone film [1] bulk MD simulations thin film MD simulations [1] B. Krause et al. Macromolecules 2002, 35, 1738

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

bulk phase diagram for C16H34/CO2 mixture [3] bead-spring model for chain molecule FENE+LJ potential [1,2] LJ potential for CO2-CO2 and non-bonded chain monomers interactions bulk phase diagram for C16H34/CO2 mixture [3] type III type I TcCO2 TcC16H34 cross-interactions between CO2 and C16H34 by LJ potential with ehc and shc using Lorentz-Berthelot mixing rule: [1] K. Kremer, G. S. Grest, JCP, 92, 5057 (1990) [2] L.G. MacDowell, P. Virnau, M. Müller, K. Binder, JCP, 117, 6360 (2002) [3] K.Binder, M.Müller, P.Virnau, L.G. MacDowell, Adv. Polym.Sci, 176, 1 (2004)

Confinement: two infinite parallel walls consisting of spherical particles interactions between fluid particles and wall particles: U r rcut 

isothermal slice through the phase diagram of C16H34/CO2 at T=486K [1] Grand canonical MC TPT1-MSA EOS [2] spinodal curve [2] molar fraction of CO2 pressure, 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 [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)

METHOD MD simulations with use of ESPResSo [1] parallelized simulation package 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 Lx=300 (135nm) Lz=15s t=0-500, t=10 t=100-3800 t=100 Lx=300 (135nm) Ly=300 (135nm) t=100 t=500 t=2000

DENSITY PROFILES IN Z DIRECTION C16H34 CO2 t=0

time dependence of characteristic length scale scaled real-space correlation function G(r,t): g(r,t)- pair correlation function

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)

Thank you for your attention! Acknowledgements Dr. Peter Virnau (Mainz) Dr. Subir Das (Mainz) Dr. Torsten Stühn (MPI Mainz) ESPResSo: Research group of C. Holm, Max Planck Institute for Polymer Research in Mainz, Germany CPU time in JUMP cluster and SOFTCOMP in Jülich Thank you for your attention!

spinodal decomposition peak DENSITY-DENSITY STRUCTURE FACTOR Snn homogeneous system before quench system after pressure quench at t=50 LJ peak spinodal decomposition peak number density structure factor: partial structure factors:

time dependence of structure factor 3rd layer at z=3.75 5th layer at z=6.75

characteristic domain size R:

3rd layer at z=3.75 t=10 t=50 t=100 t=200 5th layer at z=6.75

pressure jump: p*=0.21 to p*=0.08

RELATIVE CONCENTRATION DENSITY PROFILE TOTAL DENSITY PROFILE