On the DPD Parameter Estimation from Atomistic / Quantum Mechanics Information

On the DPD Parameter Estimation from Atomistic / Quantum Mechanics InformationMaurizio Fermeglia, Paola Posocco, Sabrina PriclMOSE Lab, Department of Chemical Engineering, University of Trieste, ItalyJan-Willem HandgraafCULGI B.V., Leiden, NetherlandsJohannes FraaijeLeiden Institute of Chemistry, Soft Matter Chemistry, University of Leiden, Netherlands.Peter Degimann, Vandana Kurkal-Siebert, Horst WeissBASF Germany.

Maurizio.fermeglia@dicamp.units.itmose.units.it

Nashville, 22 April 2023 - slide 2AIChE Annual Meeting

Outline of talkIntroduction 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

modellingGrafted nanoparticles and polymersProperties of interest mechanical, thermochemical and flow behaviour glass transition temperature.

For automotive industry

MeccanicaQuantistica(elettroni)

Meccanicamolecolar

e(atomi)

Modellazionedi

mesoscala(insiemi di

atomi o molecole)

Simulazione di

processoFEM

Engineering design

1ÅCharacteristic Length

1nm 1μm 1mm 1m

seconds

nanoseconds

picoseconds

femtoseconds

QuantumMechanics(electrons)

MolecularMechanics

(atoms)

Mesoscale modeling

(segments)

Process Simulation

Engineering design

Characteristic Time

1nm 1μm 1mm 1m

minutes

microseconds

Multiscale Molecular Modeling

Message passing multiscale

modeling

Reverse mapping

Molecular Dynamics Dissipative Particle Dynamics

ForceField based calculationsSoft potentials calculations

Fi = f (aii, aij, …, rc )

From atoms … to beads

Polymeric materials are modeledby connecting beads by harmonic springs

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 coefficientsMethod 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 systemGrafted nanoparticles and semicrystalline polymers Core: amorphous SiO2 5nm diameter Linker: Si based component Grafted polymer chains: PS 2k Polymer: semicrystlline polystirene

Carved Sphere

Etched SphereGrafted Sphere

BrC(CH3)2CO2(CH2)3SiMe2ClHO

The model system: MD representation

Grafted without bulk polymer Grafted with bulk polymer

Conclusions

405060

0 50 100 150 200

Method 1: bead size, chain architecture

MD NPT runs on homo polymers Monomer length C∞ calculation and Kuhn lenght Chain architecture22

2 NLnlCr

NLr max

Rotational Isomeric State

MM minimization and annealing

MD - NPT

<r>2 – end to end distance

<r>2 / n l2 = C∞

Change chain lenght

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:

C2K ~ 4.5

Method 1: bead size, chain architecture

3109.0ln dTCd

Method 1: DPD Interaction parametersSingle, binary, ternary

energies from MD

Interaction energiesfrom MD

(vdW + Coulomb)

Define DPD beads and

recalculate energies

Binding energies are rescaled considering the

number of contacts

Reference DPD Interactions are selected

Equal beads aii 25

Strong repulsive beads aij >25DPD matrix parameters

(scaling using reference)

Density profiles from DPDDensity profiles from MD =?

Scocchi et al., J. Phys. Chem. B, (2007), 111, 2143Posocco et al., Macromolecules 2009, online ASAP

DPD parameters validation: method 1

Comparison of density profiles obtained from atomistic MD simulations and mesoscale DPD simulations

ijijjjjjiiii

sys EnEnEnE 2

aij S L PL PM

S 15 5 30.9

L 5 24.8

PL 30.9

PM 28.3

Method 1: DPD Interaction parametersCalculation 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

Conclusions

Method 2: basic idea of COSMO-RS:Quantify interaction energies local interactions COSMO polarization

charge densities s and s‘ s‘s

DEcontact = E(s,s‘)

1) Put molecules into ‚virtual‘ conductor (DFT/COSMO)

s >> 0

s ' << 0(1)

(2)hydrogen bond

electrostat. misfit

ideal contact

3) Remove the conductor on molecular contact areas (stepwise) and ask for the energetic costs of each step.

2) Compress the ensemble to approximately right density

(3) specificinteractions

2)'(2')',( ssss effmisfit aG

}',0min{)()',( 2hbhbeffhb TcaG sssss

In this way the molecular interactions reduce to pair interactions of surfaces!

A thermodynamic averaging of many ensembles is still required!

But for molecules?Or just for surface pairs?

COSMO-RS:

Scuola Nazionale GRICU di Dottorato di Ricerca – Muravera (CA), 7-11 Giugno 2009

sigma-profiles

-0.02 -0.01 0 0.01 0.02screening charge density [e/A²]

vanillin

w ater

acetone

sigma-potential

-0.02 -0.01 0 0.01 0.02

Chemical Structure

Quantum ChemicalCalculation with COSMO

(full optimization)

s-profiles of compounds

other compounds

ideally screened moleculeenergy + screening charge distribution on surface

DFT/COSMO COSMOtherm

s-profile of mixture

s-potential of mixture

Fast Statistical Thermodynamics

Equilibrium data:activity coefficientsvapor pressure,solubility,partition coefficients

Phase Diagrams

Database of COSMO-files

(incl. all common solvents)

Flow Chart of COSMO-RS Binary Mixture of

Butanol and Water at 60° C

0.0 0.2 0.4 0.6 0.8 1.0x

y CalculatedExperiment

miscibility gap

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 structure, ab initio charge

density

Free energy of mixing

Interaction Potentials

chemical potentials from COSMO-RS - A. Klamt et al. Fluid Phase Equilib. 172 (2000), 43

BAABBBAAmix xxRTG lnln

)}1()1({)}()({ BBAABBBAAAmix xxxxxxG D

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-RSChoose reference volume (here: 1 monomer unit in PS)

LinkerPS

Quartz

DPD with ρ=3:

χ(PS-Linker)=0.13, ∆a=0.45χ(PS-Quartz)=2.25, ∆a=7.87χ(Linker-Quartz)=2.13, ∆a=7.45

AAAB naa

9.3127.3

aA-N= 1*aL-N+4*aPL-N=1*5+4*30.9=25.72

PS=bulk polymerA=linker+grafted PSN=SiO2

aij PS A NPS 25A 26.6 25.4N 28.3 25.72 15

Method 1: MD

Method 2: COSMO RSaij PS A NPS 25A 26.57 25N 25.45 26.85 15

aA-N= 1*aL-N+4*aPL-N=1*32.45+4*25.45=26.85

DPD interaction parameters

Conclusions

Morphology prediction: DPD simulation

Particle concentration: 1% - 10% w/wParticle diameter: ~ 5 nmSurface converge by defining beads on icosahedron Full coverage Partial coverage

DPD interaction parameters Method 1 Method 2

Full grafting of 2k chains in 2k bulk polymer

Nanoparticels are well dispersed No aggregation

Effect of loading

10% wt

Partial grafting (A1-N11) of 2k chains in 2k bulk polymer

10% wt

Aggregation of nanoparticelsSpherical form (incresing loading)

Full grafting of 2k chains in 13k bulk polymer

10% wt

Nanoparticels are well dispersed No aggregation

Effect of loading

Partial grafting (A1-N11) of 2k chains in 13k bulk polymer

10% wt

Aggregation of nanoparticelsSpherical form (incresing loading) Similar than for 2k chains

Comparison beween methodsFull grafting of 2k chains in 2k bulk polymer 1%

Method 1 Method 2

Comparison beween methodsFull grafting of 2k chains in 2k bulk polymer 5%

Method 1 Method 2

Comparison beween methodsPartial grafting (A1-N11) of 2k chains in 2k bulk polymer 5%

Method 1 Method 2

Lliterature

Bulk polymer 2k full coverage

Bulk polymer 13k partial coverage

Conclusions

ConclusionsMultiscale 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

AcknowledgmentsNanomodel EU Project for Financial support

On the DPD Parameter Estimation from Atomistic / Quantum Mechanics Information

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