Multiscale Simulations for Soft Matter: Applications and ... · Multiscale Simulations for Soft Matter: Applications and New Developments ... namd / Gaussian . CPMD ... lammps.sandia.gov

Multiscale Simulations for Soft Matter: Applications and New Developments

K. Kremer Max Planck Institute for Polymer Research, Mainz

Cambridge December, 03, 2015

COWORKERS: Debashish Mukherji, MPIP Aoife Fogarty, MPIP Luigi Delle Site, FU Berlin Matej Praprotnik , Ljubljana Christoph Junghans , Los Alamaos Simon Poblete , FZ Jülich Han Wang, Beijing, now FU Berlin Adolfo Poma , La Sapienza Rome, Sebastian Fritsch, MPIP Raffaelo Potestio, MPIP Davide Donadio, MPIP Karsten Kreis, MPIP Ralf Everaers, ENS Lyon Pep Espanol, Madrid Rafa Delgado Buscalioni, Madrid C. Clementi group (Rice), G. Ciccotti (Rome), …

Support: MMM Initiative of the MPG, Volkswagen Foundation, DAAD, KITP(NSF), DFG, ERC …

Soft Matter “Soft” means: - low energy density - nanoscopic length scales (10Å …1000Å) - large (conformational) fluctuations large intra molecular entropy - thermal energy kBT relevant energy scale

molkJkTmolkcalkT

cmkTpNnmkT

EkTeVkTJkT

KKJE

H

/5.2/6.0

2001.4

105.9105.2101.4

300/1038.1

1

4

2

21

23

⇒⇒⇒

≈⋅≈

⋅≈

⋅≈

⋅⋅=

−

−

−

−

−

Energy Scale kBT forT=300K

Quantum Chemistry

Electronic structure, CPMD

Biophysics Membranes, AFM

Spectroscopy

kTkTEkTJE

10480103 19

−≈≈⋅≈ − Chemical Bond

Hydrogen Bond

molkJkTmolkcalkT

cmkTpNnmkT

EkTeVkTJkT

KKJE

H

/5.2/6.0

2001.4

105.9105.2101.4

300/1038.1

1

4

2

21

23

⇒⇒⇒

≈⋅≈

⋅≈

⋅≈

⋅⋅=

−

−

−

−

−

Energy Scale kBT forT=300K

Quantum Chemistry

Electronic structure, CPMD

Biophysics Membranes, AFM

Spectroscopy

kTkTEkTJE

10480103 19

−≈≈⋅≈ − Chemical Bond

Hydrogen Bond

Soft Matter – Nanostructured Matter

Volume V= L3 A: Surface and Interface Area

Nanoscopically Structured Material: V/A << 1μm => Distinction Bulk vs Surface/Interface not useful

Definition of A usually depends on the question studied!

Time

Atomistic

Soft fluid

Local Chemical Properties --- Scaling Behavior of Nanostructures Energy Dominance --- Entropy Dominance of Properties

Finite elements

Characteristic Time and Length Scales

Length

bilayer buckles Molecular

GROMACS www.gromacs.org NAMD www.ks.uiuc.edu/Research/namd/

Gaussian CPMD

Quantum

ESPResSo++ www.epresso-pp.mpg.de VOTCA www.votca.org LAMMPS lammps.sandia.gov/

http://www.epresso-pp.mpg.de/

Multiscale Simulations for Soft Matter:

Sequential

Concurrent Tri-glycine in Urea-Water Mixture

Mukherji, van der Vegt, KK, JCTC 8, 3536 (2012).

Soft coarse-grained Atomistic

? 𝑈𝑈𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝(𝑟𝑟)

Intermediate coarse-grained

Atomistic

~ half-million atoms

Gemünden, Poelking, KK, Daoulas, Andrienko, Macromol. Rapid Com. 2015

P3HT Morphology


Sequential






Atomistic



P3HT Morphology

Sequential Multiscale Simulations :

Azo Benzene LCs C. Peter, L. Delle Site, D. Marx

BPA-PC L. Delle Site, C. Abrams K. Johnston (1998ff)

Peptides C. Peter Polystyrene,

(w/wo additives) V. Harmandaris, D. Fritz N. Van der Vegt


Coarse Graining (CG) micro - meso

Interplay Energy Entropy Free Energy Scale: kBT

atomistic model cg model Different general strategies to match : Structure (Mainz group, Lyubartsev…) Force (Ercolessi&Adams, Voth&Noid…) Relative Entropy (Shell, talk at this meeting) Potentials/Free Energies (e.g. Martini force field, Marrink) Methods to calculate CG interactions: (Iterative) Boltzmann Inversion Inverse MC, Iterative Force Matching Relative Entropy… (perspective W. Noid JCP 2013)

VOTCA: Versatile Object oriented Toolkit for Coarse-graining Applications

General ansatz: n “atomistic”, N cg particles

D. Andrienko et al, CPC 2009, www.votca.org

(Iterative) Boltzmann Inversion Inverse MC, Force Matching VOTCA test cases: SPC/E water, methanol, liquid propane, single hexane

( )

• Boltzmann inversion (example: bonded interactions)

Hendersen Theorem: unique correspondence between U(r) and g(r) Potential is state point dependent

Basic standard methods


• Iterative Boltzmann inversion

U(1)(r) = - kBT ln P(1)(r)


• Inverse Monte Carlo (Lyubartsev)

Similar concept as Boltzmann inversion, however sampling directly on the discretized potential u(r,…) Automatically includes correlations (unlike factorization ansatz for Boltzmann inversion) Numerically more demanding


Discretize distance r in postions α, Sα particles as distance α

Construct CG potential, that Sα at positions α match g(r)




• Force Matching (Ercolessi&Adams, Noid&Voth et al JCP 2008ff)

ωα parameters to locate CG bead Take L snapshots, determine coefficients for N cg particles

No direct link to underlying configurations, free energy match (up to self energy of the cg particles)


D. Andrienko et al, 2009

SPC/E Water 300K, 1bar

Liquid Methanol 300K, 1bar

VOTCA: Versatile Object oriented Toolkit for Coarse-graining Applications (Examples here: two-body forces only)

D. Andrienko et al, 2009

Liquid Propane 200K, 1bar

VOTCA: Versatile Object oriented Toolkit for Coarse-graining Applications

• Iterative Boltzmann inversion direct, needs further refining “afterwards”

• Inverse Monte Carlo more precise than IBI, includes higher order correlations, more demanding, slow convergence

• Force Matching no close link to underlying configurations, approximative solutions, needs three…body interactions, based on matching thermodynamic properties

• “other Methods” often mixed approaches for inter and intra molecular properties, other method “restricted entropy” approach (M. Scott Shell)

Comparison particle based methods

Representability and Transferability Issues

Interplay Energy Entropy Free Energy Scale: kBT

Micro-Meso Simulation

atomistic model => parameterize cg model => run/analyze large system (melt etc) “measurements” R2(N)… reintroduce details => run/analyze atomistic system

Structure Based Coarse Graining **********

Coarse Graining (CG) <=> Inverse Mapping

Coarse-graining: map bead-spring chain over molecular structure. => Many fewer degrees of freedom

Inverse mapping: grow atomic structure on top of coarse- grained backbone =>Large length-scale equilibration in an atomically resolved polymer

Structure Based Molecular Coarse-Graining: Bisphenol-A-Polycarbonate

9.3-11.5 Å

W. Tschöp, K. Kremer, J. Batoulis, T. Bürger, O. Hahn Acta Polym. 49, 61 (1998); ibid. 49, 75, ff

Speedup ≈ 104 !

Interaction Energies in the Coarse-Grained Model

• Excluded volume • Bonds • Angles • Torsions

U

P

Angle potentials are T-dependent Boltzmann inversions; e.g., at carbonate:

T = 570 K

⇐⇐⇐⇐

Coarse grained BPA-PC chain

All atom model

How good are generated conformation? Inverse Mapping:

Reintroduce Chemical Details

Structure factors of BPA-PC melt

Comparison: Simulation vs n-Scattering

22

A37)( o

G

NNR

≅

Well equilibrated coarse grained AND all atom melt configurations!

J. Eilhard et al, J. Chem. Phys. 110, 1819 (1999) B. Hess et al, Soft Matter 2006

PC at Ni Surface: Role of Chain Ends Energy - Entropy Competition

Energy Entropy

L. Delle Site et al., J.Am.Chem.Soc.; 126; 2004; 2944

Generalization: Bottom up ↔ Top down: Soft models => particle based models

Database for many specific systems

Zhang, Stuehn, Daoulas, KK, 2014, 2015

M. Böckmann, D. Marx, C. Peter, L. Delle Site, K. K., N. Doltsinis, PCCP, 2011, ff

QM & QM/MM

hν coarse grained / mesoscale classical

atomistic

hν

Trans-8AB8 liquid crystal

cis/trans mixture

Photoinduced LC phase transition

length

time

Example LC phase transition: 8AB8

Example LC phase transition

Aim: Construct CG model that: Reproduces the atomistic (thermotropic) phase behavior Reproduces atomistic structures (incl. box-aspect ratio/pressure anisotropy)

Target state point: LC system just below the thermotropic phase transition smectic system @ 460 K

Tiso>SmA

➭Find: suitable isotropic reference system

Example LC phase transitions SmA @ 460 K Disordered @ 480 K

Super-cooled fluid @ 460 K Just below Tc

CG model should reproduce this transition !

Parametrisation impossible here:

(layering built into potentials)

CG model should reproduce structure

overall isotropic residual nematic order

Parametrise HERE!!

fully ordered system: (not good for parameterization)

isotropic systems (residual local order)

ri rj

u(ri) u(rj)

Example LC phase transitions

globally isotropic super-cooled liquid

with local order

Super-cooled fluid @ 460 K

Mukherjee, Delle Site, KK, Peter JPC B 2012

Example LC phase transitions

Mukherjee, Delle Site, KK, Peter JPC B 2012

➮CG model reproduces LC structure …

orde

ring

alon

g z

axis

CG model

backmapped atomistic

atomistic

atomistic

CG (new model)

backmapped atomistic

CG (old model, fragment-based)

nem

atic

ord

er p

aram

eter

MD, SCMF Processing Nonequilibrium


• robust, versatile for “simple” systems (amorphous polymers, LC systems…)

• CG potentials state point dependent ⇒ transferability and representability issues of interactions (example isotropic smectic transition in 8AB8 LC systems) Length scale mapping obvious, but time scale…

• Scaling of dynamics

• Amorphous polymer melt (PS) • Smectic LC system (8AB8)


• Scaling of dynamics • Amorphous polymer melt (PS)


• Scaling of dynamics • Amorphous polymer melt (PS)

Mapping times for short distance displacements (≈ 10 – 20 Å): 400 ps (AA sim) ↔ 1τLJ (CG sim)

Experiment: Raw FRS data, Sillescu

Simulation: NO adjustable parameter

V. Harmandaris, KK, Soft Matt. 2009

≠

dominates dynamics


• Scaling of dynamics • Smectic LC system (8AB8) • In-plane diffusion

• Direct jump between layers • Parking lot jump mechanism


• Scaling of dynamics • Smectic LC system (8AB8)

• In-plane diffusion • Direct jump between layers • Parking lot jump mechanism

parking lot direct

Free energy surface CG AA

z

Cos θ


• Scaling of dynamics • Smectic LC system (8AB8)

• In-plane diffusion • Direct jump between layers • Parking lot jump mechanism

Process CG Atomistic

Jump time (straight)

0.15 τ 0.2 ns

Jump time (pkl) Timestraight/ Timepkl

1.7 τ 0.088

1.0 ns ≠ 0.2

⇒ Severe problems for structure formation etc

Free energy surface CG AA

z

Cos θ

M. Deserno et al., Nature, 2007 Andrienko et al,

PRL 98, 227402 (2007) C. Peter et al, 2008ff

Standard Sequential Approach: Run whole system on one level of resolution.

Do we always need/want to do that?


Sequential






Atomistic



P3HT Morphology

AdResS Adaptive Resolution MD Simulation

Theory: M. Praprotnik, KK, L. Delle Site, PRE 75, 017701 (2007), JPhys A MathTh F281 (2007)

Method: Praprotnik, Delle Site, KK: J. Chem. Phys. 123, 224106 (2005) & Phys. Rev. E 73, 066701 (2006)

Requirements (for zooming in) Same mass density (?) Same temperature (?) No free energy barriers Smooth transition forces Same center-center g(r) (?)

Free exchange between regimes

(Simple two body potential)

⇒ “Some similarities” to 1st order phase transition ⇒ “Phase equilibrium”

Adaptive Methods: Changing degrees of freedom (DOFs) on the fly

VW Foundation Project M. Praprotnik, L. DelleSite, KK, JCP 2005, PRE (2006)

Free exchange between regions: Structure based CG - Compressibility

SPC/E water, cg based on matching g(r)

Pressure

Compressibility

Equation of State: Pressure Correction

Structure based CG, based on g(r) - pressure corrected

p

V

Structure based CG, based on g(r) - pressure corrected

p

V

Equation of State: Pressure Correction

Structure based Coarse Graining: Perfect match of g(r) all atom – coarse grained κatomistic = κcg BUT pcg = 6200patomistic

Test case: Coarse Grained Water: SPC/E

Compensation forces between regions needed

Adaptive Methods:

Requirements: • Free exchange of molecules • NO (free) energy barriers • Smooth transition forces • Structure and dynamics preserved

• (at least in all atom region)

Different Interpolation schemes: • Force should be antisymmetric on exchange of particles α ↔ β, => Newton 3rd law • Force interpolation, no Hamiltionian

• Energy interpolation, MC possible, Ensembles → Newton 3rd law not exactly fulfilled

JCP 2005, PRL 2012,2013, Ann Rev Phys Chem 2008

How to couple all-atom and coarse-grained models?

Transition Regime – Interpolation of Energy Uαβ?

cgatom UXWXwUXwXwU αββααββααβ )]()(1[)()( −+=

Full atomistic potential Full coarse grained potential

Fαβ ≠ -Fβα

β

cgatom UXWXwUXwXwU αββααββααβ )]()(1[)()( −+=

Full atomistic potential Full coarse grained potential

• Drift terms from W(x) • Violation of Newton’s 3rd law • Mathematical inconsistencies at boundaries

• There exists no W(x), such that forces become conservative (L. Delle Site PRE 2007) => Force interpolation

Transition Regime – Interpolation of Energy Uαβ?

AdResS: Transition Regime - Force Interpolation

cgatom FXWXwFXwXwF αββααββααβ )]()(1[)()( −+=

Interactions explicit-explicit CG-CG hybrid-hybrid CG- hybrid: CG-CG explicit-hybrid: explicit-explicit

Full atomistic force Full coarse grained force

Similar ansatz: Ensing et al JCTC 2007

AdResS: Transition Regime - Force Interpolation

cgatom FXWXwFXwXwF αββααββααβ )]()(1[)()( −+=

Interactions explicit-explicit CG-CG hybrid-hybrid CG- hybrid: CG-CG explicit-hybrid: explicit-explicit

Full atomistic force Full coarse grained force Transition regime: Force interpolation (Newtons 3rd law fulfilled, no drift forces) No transition energy function defined! Pressure, Temperature, Density everywhere well defined Thermostat needed (no microcanonical simulation possible!)

* Similar problem already in H.C. Andersen, JCP 72, 2384 (1979)

Theoretical Basis: Temperature… Necessity of Thermostat

Special Example: Two spherical particles, same EoS and same number DOFs

=

p

V

Extensive theoretical work by L. Delle Site

Transition between models/levels of description => change in Free Energy

• Temperature well defined in whole box, fixed by thermostat

• Densities well defined • Forces well defined => virial pressure well defined

A unified framework for Force-Based & Energy-Based Adaptive Resolution

Simulations

Additive instead of multiplicative coupling

Mixed Hamiltonian:

Potestio et. al., Phys. Rev. Lett. 110, 108301 (2013)

Fritsch et. al., Phys. Rev. Lett. 108, 170602 (2012)

Hamiltonian scheme

Hamiltonian scheme

Idea: use weighted energy of each molecule and not forces

• Force interpolation:

• Additive force interpolation! Newton’s 3rd law fulfilled!

Potestio et. al., Phys. Rev. Lett. 110, 108301 (2013) Fritsch et. al., Phys. Rev. Lett. 108, 170602 (2012)

Energy Interpolation vs. Force Interpolation

Energy-based scheme leads to undesired drift force

Mixed Hamiltonian:

Forces:

• Model :

• Model : Potestio et. al., Phys. Rev. Lett. 110, 108301 (2013)

Energy-based scheme leads to undesired drift force

Mixed Hamiltonian:

Forces:

Potestio et. al., Phys. Rev. Lett. 110, 108301 (2013)

Violates Newton III

(looks like background field or force ramp)

H-AdResS multiscale simulation scheme

Drift term can be removed in average by adding an Hamiltonian term (background field)


Practice: determine shape of ΔH iteratively, total integral remains unchanged.



• Model :

• Model :

From H-AdResS to AdResS

Mixed Hamiltonian:

Forces:

Drift Forces decorrelate faster than Positions

• Position autocorrelation:

• Drift Force autocorrelation (averaged over all values for ):

Drift Force autocorrelations as functions of λ

Drift Force is a zero-average fluctuating force with finite, short autocorrelation time

Drift Force autocorrelations as functions of λ

Apply Colored Noise to cancel the Drift Force

• Apply colored noise with memory , which instantaneously and exactly cancels the drift force, i.e.

• We obtained a force-based model

introduction of an autocorrelated Absence of drift force random noise in a Hamiltonian

energy-conserving scheme

Thermostating model with a GLE

• To enforce thermal & mechanical equilibrium, the autocorrelated random noise must be balanced by a history-dependent friction term:

Thermostat model with a

Generalized Langevin Equation:

Equivalence of Energy-based and Force-based Models

Hamiltonian scheme thermostated with GLE

Force-based model with history-dependent friction term

Removal of Drift Force from Hamiltonian: Non-Markovian behavior whether system in

thermal equilibrium or not

Applications, Extensions

• Coupling to an ideal gas • Path integral quantum description • Large solutes in solvents • Cosolvent Effects for (Bio-) Polymers

‘stimuli responsive’ or ‘smart polymers’

Free energy compensation in transition zone allows coupling to ideal gas




Path integral quantum AdResS

See also Argawall & Delle Site JCP et al 143, 094102 (2015 )

Path integral quantum AdResS

Classical – quantum: vary mass of particles in pearls

K. Kreis, M. Tuckerman, D. Donadio, KK, R. Potestio ,2015

Interpolate between quantum (light mass m) and classical particle (heavy mass M) 0 ≤ λ ≤ 1 Feynman: quantum particle as a classical ring polymer of light particles of mass m




Applications

• Large solutes in solvents • Cosolvent Effects for (Bio-) Polymers


Structure based Coarse Graining: Perfect match of g(r) all atom – coarse grained κatomistic = κcg BUT pcg = 6200patomistic

Test case: Coarse Grained Water: SPC/E

Compensation forces between regions needed

Coarse Grained Water: SPC/E

Structure based Coarse Graining: apply pressure based thermodynamic correction force

coarse grained hybrid explicit coarse grained hybrid explicit

Example SPC/E water

Hydrophobic Solutes

C60

C2160

Influence of bulk H-bond structure on surface layer # two surface potentials - standard (weak) Lennard Jones (εCO=0.2kBT, σCO=0.34nm) - purely repulsive (r-12) # variable width of explicit layer

Transition layer All atom layer, dex

Hydrophobic Solutes: Surface vs Bulk CG regime

Water

cg water reproduces g(r) but NOT tetrahedral packing!

B. P. Lambeth, C. Junghans, KK, C. Clementi, L. Delle Site, JCP 2010

Application: Ubiquitin in Water

• Ubiquitin in water, …

A. C. Fogarty, R. Postestio, KK, JCP 2015

• Ubiquitin in water, …

A. C. Fogarty, R. Postestio, KK, JCP 2015

Only TWO layers of explicit water needed to properly reproduce B-factors!

Application: Ubiquitin in Water

Application: HEWL - Hen Egg White Lysozyme Combining AdResS with Elastic Network Models

A. C. Fogarty, R. Postestio, KK, submitted 2015

ENM – AA model AdResS setup

Applications

• Large solutes in solvents • Cosolvent Effects for (Bio-) Polymers


Co (Non-) Solvency of Poly(NIPAm) in Water Alcohol Mixtures

- Water and alcohol are both good solvents - water and alcohol are miscible

Bischofberger et al. Soft Matter 10,8288 (2014)

‘good’ ‘poor’ ‘good solvent’

Temperature fixed


- Water and alcohol are both good solvents - water and alcohol are miscible

Bischofberger et al. Soft Matter 10,8288 (2014)

‘good’ ‘poor’ ‘good solvent’

Two mixed good solvents result in a poor solvent How can this be possible?

Example: Poly(NIPAm) in aqueous alcohol

Zhang and Wu, Physical Review Letters 86, 822 (2001). Mukherji and Kremer, Macromolecules 46, 9158 (2013).

• Alcohol and water both good solvents • Alcohol and water well miscible • Pure water: chain expanded • Pure alcohol: chain expanded • Mixture: chain collapses

hydrophobic hydrophilic hydrophobic


Fluctuation theory: Global thermodynamic properties from microscopic (pair-wise) molecular distributions

Kirkwood and Buff, J. Chem. Phys. 19, 774 (1951).

∆Nij = ρ jGij

Excess (depletion) coordination number ⇒ Grand canonical ensemble (or needs very large systems)

- Solvation energy - Partial molar volume - Activity coefficient - Compressibility …….

Fluctuation theory of Kirkwood-Buff

Fluctuation theory of Kirkwood-Buff So

lvat

ion

Free

Ene

rgie

s

Kirkwood and Buff, J. Chem. Phys. 19, 774 (1951).

Semi Grand Canonical AdResS

D. Mukherji, KK, Macromolecules, 2013

Exchange water and alcohol

6.4 nm

N ~ 6000 molecules

Exchange region Periodic boundary conditions

Semi Grand Canonical AdResS

D. Mukherji, KK, Macromloecules, 2013

Exchange water and alcohol

6.4 nm

N ~ 6000 molecules

Exchange region Periodic boundary conditions

Poly-NIPAm chemical potential shift

“expected shape”

Mukherji and Kremer, Macromolecules (2013)

100% water 100% alc.

“expected shape”


Poly-NIPAm chemical potential shift

100% water 100% alc.

Poly-NIPAm chemical potential


water -> alcohol solvent chain collapses in better good solvent

Poly-NIPAm in aqueous methanol

Mukherji, KK, Macromolecules (2013) Mukherji, Marques,KK, Nat. Comm. (2014), JCP (2015)

Conclusion / Challenges

• Dual-Triple… Scale Simulations/Theory – Adaptive quantumforce fieldcoarse grained … – Grand Canonical i.e. salt etc

• Nonbonded Interactions: NEMD, Structure Formation, Morphology…

• Conformations Electronic/Optical Properties • Structure Formation, Aggregation, Dynamics • Online Experiments:

– Nanoscale Experiments, long Times

Conclusion / Challenges

• Dual-Triple… Scale Simulations/Theory – Adaptive quantumforce fieldcoarse grained … – Grand Canonical i.e. salt etc

• Nonbonded Interactions: NEMD, Structure Formation, Morphology…

• Conformations Electronic/Optical Properties • Structure Formation, Aggregation, Dynamics • Online Experiments:

– Nanoscale Experiments, long Times

Materials are the result of non equilibrium processes

PostDoc and PhD Student positions available http://www.mpip-mainz.mpg.de/polymer_theory

Documents

Multiscale Simulations for Soft Matter: Applications and ... · Multiscale Simulations for Soft Matter: Applications and New Developments ... namd / Gaussian . CPMD ... lammps.sandia.gov