On the DPD Parameter Estimation from Atomistic / Quantum Mechanics Information

On the DPD ParameterEstimationfromAtomistic / Quantum Mechanics Information Maurizio Fermeglia, Paola Posocco, Sabrina Pricl MOSE Lab, Department of Chemical Engineering, University of Trieste, Italy Jan-Willem Handgraaf CULGI B.V., Leiden, Netherlands Johannes Fraaije Leiden Institute of Chemistry, Soft Matter Chemistry, University of Leiden, Netherlands. Peter Degimann, Vandana Kurkal-Siebert, Horst Weiss BASF Germany. Maurizio.fermeglia@dicamp.units.it mose.units.it

Outline of talk Introduction Multiscale molecular modeling The reference system DPD parameters calculation via MD Interaction energies calculation, mapping to mesoscale DPD parameters calculation via COSMO-RS COSMO-RS fundamentals and mapping procedure Results Mesoscale simulations using DPD Nanostructure estimation Comparisons Conclusions

Motivation: modelling of nanocomposites • EU FP7: Multi-Scale Modelling of Nano-Structured Polymeric Materials: From Chemistry to Materials Performance • Models for reference systems  elucidate structure-property relationships • Development of new materials based on Multiscale modelling • Grafted nanoparticles and polymers • Properties of interest • mechanical, thermochemical and flow behaviour • glass transition temperature. • For automotive industry

Multiscale Molecular Modeling Characteristic Time Engineering design Engineering design years Message passing multiscale modeling hours Process Simulation FEM Simulazione di processo FEM minutes Mesoscale modeling (segments) Modellazione di mesoscala (insiemi di atomi o molecole) seconds Reverse mapping microseconds MolecularMechanics (atoms) Meccanica molecolare (atomi) nanoseconds picoseconds QuantumMechanics (electrons) Meccanica Quantistica (elettroni) femtoseconds 1μm 1μm 1Å 1Å 1nm 1nm 1mm 1mm 1m 1m Characteristic Length

From atoms … to beads Polymeric materials are modeledby connecting beads by harmonic springs Molecular Dynamics Dissipative Particle Dynamics Soft potentials calculations Fi = f (aii, aij, …, rc ) ForceField based calculations

From atomistic to mesoscale .. The parameters for Mesoscale are the bead size and Gaussian chain architecture the effective Flory-Huggins interactions the bead mobilities M (not for DPD) Method 1: MD bead size and Gaussian chain architecture: by MD from characteristic ratio (C) in terms of Kuhn length Interaction parameters from energy distribution in MD Considering density distribution around nanofiller mobility: by Molecular Dynamics Bead self diffusion coefficients Method 2: COSMO RS bead size and Gaussian chain architecture: Splitting the chain into beads of equal volume Interaction parameters from continuum salvation models (COSMO RS) QM calcualtions to get the Flory Huggins interaction parameter mobility: by Molecular Dynamics Bead self diffusion coefficients

The model system Grafted nanoparticles and semicrystalline polymers Core: amorphous SiO2 5nm diameter Linker: Si based component Grafted polymer chains: PS 2k Polymer: semicrystlline polystirene BrC(CH3)2CO2(CH2)3SiMe2Cl Carved Sphere Etched Sphere Grafted Sphere

The model system: MD representation Grafted without bulk polymer Grafted with bulk polymer

Method 1: bead size, chain architecture MD NPT runs on homo polymers Monomer length C∞ calculation and Kuhn lenght Chain architecture Rotational Isomeric State C1 C2 C3 C4 Cn MM minimization and annealing Change chain lenght MD - NPT <r>2 – end to end distance <r>2 / n l2 = C∞ C∞ Fermeglia, M. et al., Polymer, 47:5979-5989 (2006) Posocco et al., Macromolecules 2009, online ASAP

C for 2K at 448K corrected for temperature effect to 358K: The number of DPD beads for each PS 2K chain: Method 1: bead size, chain architecture C2K ~ 4.5

Method 1: DPD Interaction parameters Single, binary, ternaryenergies from MD Binding energies are rescaled considering the number of contacts Interaction energiesfrom MD (vdW + Coulomb) Reference DPD Interactions are selected Equal beads aii 25 Define DPD beads and recalculate energies Strong repulsive beads aij >25 DPD matrix parameters(scaling using reference) Scocchi et al., J. Phys. Chem. B, (2007), 111, 2143 Posocco et al., Macromolecules 2009, online ASAP Density profiles from MD Density profiles from DPD =?

DPD parameters validation: method 1 • Comparison of density profiles obtained from atomistic MD simulations and mesoscale DPD simulations

Method 1: DPD Interaction parameters Calculation of DPD parameters from MD For the system SiO2/LPS2K/PS2K MD simulations NVT (5 ns – 358 K - 10 conformations) Estimation of Interaction Energies Calculation of energy per bead  aij PM PL L L S

Method 2: basic idea of COSMO-RS: Quantify interaction energies local interactions COSMO polarization charge densities s and s‘ s s‘ s‘ s DEcontact = E(s,s‘)

COSMO-RS: s >> 0 s ' << 0 + + _ _ _ s + _ + _ + s ' + 1) Put molecules into ‚virtual‘ conductor (DFT/COSMO) 2) Compress the ensemble to approximately right density 3) Remove the conductor on molecular contact areas (stepwise) and ask for the energetic costs of each step. In thiswaythemolecularinteractionsreduceto pair interactionsofsurfaces! (2) hydrogen bond (1) electrostat. misfit A thermodynamicaveragingofmanyensemblesis still required! But formolecules? Or just forsurfacepairs? ideal contact (3) specific interactions Scuola Nazionale GRICU di Dottorato di Ricerca – Muravera (CA), 7-11 Giugno 2009

Chemical Structure Flow Chart of COSMO-RS Phase Diagrams Equilibrium data: activity coefficients vapor pressure, solubility, partition coefficients Quantum Chemical Calculation with COSMO (full optimization) s-potential of mixture s-profiles of compounds ideally screened molecule energy + screening charge distribution on surface Fast Statistical Thermodynamics Database of COSMO-files (incl. all common solvents) other compounds s-profile of mixture DFT/COSMO COSMOtherm

Method 2: Flory-Huggins-like parameter Details on calculations DFT-calculations with TURBOMOLE Becke-Perdew-86 functional (BP86) within the RI-J approximation using a TZVP-basis set COSMOtherm release C2.1 (Rev. 01.05) chemical potentials from COSMO-RS - A. Klamt et al. Fluid Phase Equilib.172 (2000), 43 Free energy of mixing Interaction Potentials Chemical structure, ab initio charge density

Interaction Parameters for „Hairy“ Quartz Nanoparticels in a PS Matrix Start from molecular models PS, Linker: use cut Quartz: use cluster model Compute interaction thermodynamics of relevant surfaces via COSMO-RS Choose reference volume (here: 1 monomer unit in PS) DPD with ρ=3: χ(PS-Linker)=0.13, ∆a=0.45 χ(PS-Quartz)=2.25, ∆a=7.87 χ(Linker-Quartz)=2.13, ∆a=7.45 PS Linker Quartz

DPD interaction parameters Method 1: MD PS=bulk polymer A=linker+grafted PS N=SiO2 aA-N= 1*aL-N+4*aPL-N=1*5+4*30.9=25.72 Method 2: COSMO RS aA-N= 1*aL-N+4*aPL-N=1*32.45+4*25.45=26.85

Morphology prediction: DPD simulation Particle concentration: 1% - 10% w/w Particle diameter: ~ 5 nm Surface converge by defining beads on icosahedron Full coverage Partial coverage DPD interaction parameters Method 1 Method 2 PL L

Nanoparticels are well dispersed No aggregation Effect of loading Full grafting of 2k chains in 2k bulk polymer 1% wt 5% wt 10% wt

Partial grafting (A1-N11) of 2k chains in 2k bulk polymer 1% wt 5% wt Aggregation of nanoparticels Spherical form (incresing loading) 10% wt

Full grafting of 2k chains in 13k bulk polymer 1% wt 5% wt • Nanoparticels are well dispersed • No aggregation • Effect of loading 10% wt

Partial grafting (A1-N11) of 2k chains in 13k bulk polymer 1% wt 5% wt • Aggregation of nanoparticels • Spherical form (incresing loading) • Similar than for 2k chains 10% wt

Comparison beween methods • Full grafting of 2k chains in 2k bulk polymer 1% Method 2 Method 1

Comparison beween methods • Full grafting of 2k chainsin 2k bulk polymer 5% Method 2 Method 1

Comparison beween methods • Partial grafting (A1-N11) of 2k chainsin 2k bulk polymer 5% Method 2 Method 1

Lliterature • Bulk polymer 2k full coverage • Bulk polymer 13k partial coverage

Conclusions Multiscale molecular modeling for nanoparticels dispersion in polymers Method 1: based on MD Method 2: based on COSMO RS Two methods give similar results Reference system of grafted SiO2 nanoparticels Morphology in agreement with literature data MD method Solid, reliable and of wide applicability Validated mesoscale structures versus atomistic simulations Applicable to a wide variety of nanoobjects (PCN, CNT, minerals, TiO2, SiO2,…) COSMO RS method much faster than MD If DFT is available Bead size and chain architecture is arbitrary Needs further validation at mesoscale Very promising approach

Acknowledgments • Nanomodel EU Project for Financial support

On the DPD Parameter Estimation from Atomistic / Quantum Mechanics Information