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On the DPD Parameter Estimation from Atomistic / 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 - PowerPoint PPT Presentation
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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.
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
Nashville, 22 April 2023 - slide 3AIChE Annual Meeting
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
Nashville, 22 April 2023 - slide 4AIChE Annual Meeting
MeccanicaQuantistica(elettroni)
Meccanicamolecolar
e(atomi)
Modellazionedi
mesoscala(insiemi di
atomi o molecole)
Simulazione di
processoFEM
Engineering design
1ÅCharacteristic Length
1nm 1μm 1mm 1m
years
seconds
nanoseconds
picoseconds
femtoseconds
QuantumMechanics(electrons)
MolecularMechanics
(atoms)
Mesoscale modeling
(segments)
Process Simulation
FEM
Engineering design
1Å
Characteristic Time
1nm 1μm 1mm 1m
hours
minutes
microseconds
Multiscale Molecular Modeling
Message passing multiscale
modeling
Reverse mapping
Nashville, 22 April 2023 - slide 5AIChE Annual Meeting
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
Nashville, 22 April 2023 - slide 6AIChE Annual Meeting
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
Nashville, 22 April 2023 - slide 7AIChE Annual Meeting
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
HOOH
OH
BrC(CH3)2CO2(CH2)3SiMe2ClHO
OOH
SiMe2
O
OBr
3
Nashville, 22 April 2023 - slide 8AIChE Annual Meeting
The model system: MD representation
Grafted without bulk polymer Grafted with bulk polymer
Nashville, 22 April 2023 - slide 9AIChE 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
Nashville, 22 April 2023 - slide 10AIChE Annual Meeting
010
2030
405060
7080
90100
0 50 100 150 200
N
Cinf
(%)
Method 1: bead size, chain architecture
MD NPT runs on homo polymers Monomer length C∞ calculation and Kuhn lenght Chain architecture22
0
2 NLnlCr
NLr max
Rotational Isomeric State
C1
C2
C3
C4
Cn
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
Nashville, 22 April 2023 - slide 12AIChE Annual Meeting
C for 2K at 448K corrected for temperature effect to 358K:
The number of DPD beads for each PS 2K chain:
C2K ~ 4.5
42
K
b CNN
Method 1: bead size, chain architecture
3109.0ln dTCd
Nashville, 22 April 2023 - slide 13AIChE Annual Meeting
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
Nashville, 22 April 2023 - slide 14AIChE Annual Meeting
DPD parameters validation: method 1
Comparison of density profiles obtained from atomistic MD simulations and mesoscale DPD simulations
Nashville, 22 April 2023 - slide 15AIChE Annual Meeting
ijijjjjjiiii
tot
sys EnEnEnE 2
aij S L PL PM
S 15 5 30.9
28.3
L 5 24.8
30.6
28.1
PL 30.9
30.6
25.6
26.2
PM 28.3
28.1
26.2
25
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
Nashville, 22 April 2023 - slide 16AIChE 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
Nashville, 22 April 2023 - slide 17AIChE Annual Meeting
Method 2: basic idea of COSMO-RS:Quantify interaction energies local interactions COSMO polarization
charge densities s and s‘ s‘s
ss‘
DEcontact = E(s,s‘)
Nashville, 22 April 2023 - slide 18AIChE Annual Meeting
1) Put molecules into ‚virtual‘ conductor (DFT/COSMO)
++
++
++
__
__ _
s '
s
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
Nashville, 22 April 2023 - slide 19AIChE Annual Meeting
sigma-profiles
0
2
4
6
8
10
12
14
-0.02 -0.01 0 0.01 0.02screening charge density [e/A²]
vanillin
w ater
acetone
sigma-potential
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
-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
1.0
0.0 0.2 0.4 0.6 0.8 1.0x
y CalculatedExperiment
miscibility gap
Nashville, 22 April 2023 - slide 20AIChE Annual Meeting
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
Nashville, 22 April 2023 - slide 21AIChE Annual Meeting
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
ABDPD
AAAB naa
51.0
9.3127.3
Nashville, 22 April 2023 - slide 22AIChE Annual Meeting
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
Nashville, 22 April 2023 - slide 23AIChE 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
Nashville, 22 April 2023 - slide 24AIChE Annual Meeting
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
Nashville, 22 April 2023 - slide 25AIChE Annual Meeting
Full grafting of 2k chains in 2k bulk polymer
Nanoparticels are well dispersed No aggregation
Effect of loading
1% wt
5% wt
10% wt
Nashville, 22 April 2023 - slide 26AIChE Annual Meeting
Partial grafting (A1-N11) of 2k chains in 2k bulk polymer
1% wt
5% wt
10% wt
Aggregation of nanoparticelsSpherical form (incresing loading)
Nashville, 22 April 2023 - slide 27AIChE Annual Meeting
Full grafting of 2k chains in 13k bulk polymer
1% wt
5% wt
10% wt
Nanoparticels are well dispersed No aggregation
Effect of loading
Nashville, 22 April 2023 - slide 28AIChE Annual Meeting
Partial grafting (A1-N11) of 2k chains in 13k bulk polymer
1% wt
5% wt
10% wt
Aggregation of nanoparticelsSpherical form (incresing loading) Similar than for 2k chains
Nashville, 22 April 2023 - slide 30AIChE Annual Meeting
Comparison beween methodsFull grafting of 2k chains in 2k bulk polymer 1%
Method 1 Method 2
Nashville, 22 April 2023 - slide 31AIChE Annual Meeting
Comparison beween methodsFull grafting of 2k chains in 2k bulk polymer 5%
Method 1 Method 2
Nashville, 22 April 2023 - slide 32AIChE Annual Meeting
Comparison beween methodsPartial grafting (A1-N11) of 2k chains in 2k bulk polymer 5%
Method 1 Method 2
Nashville, 22 April 2023 - slide 33AIChE Annual Meeting
Lliterature
Bulk polymer 2k full coverage
Bulk polymer 13k partial coverage
Nashville, 22 April 2023 - slide 34AIChE 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
Nashville, 22 April 2023 - slide 35AIChE Annual Meeting
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
Nashville, 22 April 2023 - slide 36AIChE Annual Meeting
AcknowledgmentsNanomodel EU Project for Financial support