Density Functional

Theory Simulations

in Polymer Research

Jan Andzelm

Macromolecular Science & Technology Branch

Materials & Manufacturing Science Division

Weapons & Materials Directorate

Army Research Laboratory

Aberdeen Proving Ground, MD

2012 Army Research Office Workshop

Dispersion Interactions and

Density Functional Theory

at Delaware University

Tissue Surrogates / Ballistic Testing

Why Polymers?

• “Polymers arguably represent the most important class of

materials today; their multiple and tunable attributes underpin

expanding use across most advanced technology platforms.”

– Quoting from the report of a recent polymers workshop hosted by NSF and

cosponsored by AFOSR, ARO, ONR, DOE, NASA, NIH, NIST and

Macromolecules (2009) 42(2) 465

• Polymers are pervasive in military systems

Soldier Protection Flexible

Sensors

Membranes,

filtration,

decontamination

Flexible

armor

Engineered

Multifunctional

Fabrics

Armor / structure

Coatings

Tough, durable,

soft “body” Controllable

adhesion

Soft actuators,

“artificial muscles”

Integrated soft

sensors

electronics

Robotics

Vehicles Electronics,

Power ,

Energy

Device Encapsulation

1 mm

Technical Challenges in Multiscale Modeling of Polymers

Figure, courtesy of K.Kremer

• Need to span vast length and time scales

• Need for variety of methods, appropriate for

various scales

Desig

n

Unders

tandin

g

Challenges in Modeling of

Macromolecules:

Energy vs. Entropy

Chemistry vs. Chain Dynamics

Entanglements, Networks

Self-assembly, crystallization

Strain hardening, crazing, fracture

Glassy vs. Rubbery, Tg

MACRO

MESO/

MICRO

P

Instron

How the multiscale modeling of

polymers works?

Ψ2

Atoms:

Oxygen

Carbon

Ψ

Interaction: SO3H - H2O

Hydrogen

1 nm 1 μm meters distance

1 ns 1s hours time

Electrons Atoms Grains Slip-link Fields Finite-

Elements

Molecular

builder

Experiment: • Molecular formula

Experiment: • Length, Connectivity & architecture

of polymer

Monte

Carlo

Multiscale input:

The Nobel Prize in Chemistry 1974, Paul J. Flory

No. Entanglements

Multiscale flow of data:

Force-field

Structure,

Forces

Solubility ~

interactions

Water dimer interaction components

Exchange

Electrostatic

3-rd order

Total

Dispersion

Induction

E.M. Mas, K. Szalewicz, R. Bukowski, and B. Jeziorski JCP 107, 4207 (1998).

Intermolecular interactions

in polymers

Soldier protective clothing sulfonated styrene with water and hydronium ion

Water and DFP interaction with hydroxyl and amine groups

Tissue surrogates Non-aqueous Gels; hydrocarbons

Polyurethane urea (PUU) Optimization of hydrogen bonding in hard segments

Why epoxy with lower number of cross-links may be stronger?

Equation of states Role of dispersion forces

NLO properties of chromophores DFT good for excited states and interactions

Passivation of semiconductor surfaces DFT Band structure

Protective Clothing for Soldiers

Block Copolymer as a candidate for

permeable membrane:

sulfonated S-SIBS

Polyisobutylene (IB)

Polystyrene (PS)

Sulfonated styrene Our publications:

DTRA Conference, 2009, 2010

Int. J. Multiscale Comp. Engineering, 5, 3, 2007

Mol. Simulations, 32, 163, 2006

Force Field

Development

Multiscale modeling of Permeable Membranes

Interaction of

Segments, χ

Density of

Segments

Chemical reactions, spectroscopy

Structure, Density, Diffusion

Morphology

Permeability

Mechanical p.

Tools:

Density Functional Theory

Monte Carlo & Molecular Dynamics

Dynamic Density Functional Method

Finite Element Analysis

QSAR

length

tim

e

QM

MD

MESO

MACRO

Selecting and Validating force-field

SO3H or SO3-

What is the model of a dry membrane

How many water molecules are needed to support SO3-

Chemical reactions of water

and sulfonate groups

Spontaneous dissociation

of proton (from SO3H)

occurs in the presence of

minimum three water

molecules.

The hydrogen bonds with

oxygens of the sulfonate

group are formed.

If there are less than 3 waters

present, hydronium ion

spontaneously looses

proton to sulfonate anion!

Four water

molecules (or

more) allow

for hydronium

ion to drift

away from a

sulfonate

group

Water clusters stabilized

by hydrogen bonds

interact with sulfonate

anion with energy about

120 kcal/mol

Dry S-SIBS may contain

3 waters/sulfonate (SO3- )

Use SO3- Not SO3H in MD simulations !

Hydrogen bonding in models of polymer

monomers and water: QM Study

Amine interacts with water more strongly than Hydroxyl

Hydrogen bonding (kcal/mol)

Amine-Water Hydroxyl-Water Water-water

M05/631G**/gas phase -7.6 (-3.1) -6.1 (-5.2) -5.8

M05/6-311++G**/water -5.1 (-1.1) -3.3 (-2.6) -3.4

-5.1 kcal/mol -3.3

-1.1 kcal/mol -2.6

1.89Å 1.84Å

water

gas

First step of DFP hydrolysis reaction

First (most important) step of DFP hydrolysis: insertion of DFP and attaching H to O=P to form HO-P

J.B. Wright, W.E. White, J. Mol Structure, 454 (1998) 259; J.B. Wright et al, ECBC/TR-434 (2005),

J. Andzelm, J. Walker, H. Gibson, DTRA (2010)

Barriers (kcal/mol)

for direct insertion:

NH2 (34.9)

or

H2O (33.5 & 32.1) (J.B. Wright et al.)

Method: DMol3/PBE/DNP/Cosmo(water)/LSTQST,NEB

Concerted reaction involving NH2 and H2O (Energy barrier: 26.8 kcal/mol)

Stabilization of TS by

hydrogen bonds and NH3+

Concerted insertion of

water into DFP, in the

presence of amine is a

preferable pathway

This conformation

is more stable by 4.1 kcal/mol

QM/MM Minimum Free Energy Path (QM/MM-MFEP) !

Comparison of ARL Gels & Bio-Tissue

Pig Brain Synthetic Gel

Similar mechanical response

Synthetic

Gel

Pig Brain

Socrate (MIT/ISN)

• Demonstrated potential to exploit entanglements to

mimic bio-tissue response

• “Match” to pig brain, rat heart (up to ~ 20 s-1)

• Need stronger frequency dependence to capture

higher rates (softer - low rates / stiffer - high rates)

• Coupling entangled dangling ends in network with

solvent molecular weight

projectile

Damage path

Tissue surrogates Robotics

Soft actuators, soft sensors,

durable soft “body”

Coarse-grained simulations

Morphology of

Block copolymer

Strain hardening

due to

entanglements

Branched Polymers Entangled

Our publications:

Building and equilibrating polymer melts with

entangled, branched polymers

Chem. Phys. Lett., 523,139 (2012)

Extending DPD to study mechanical deformations

J. Chem. Phys., 136, 134903 (2012)

J. Pol. Science B: Pol. Physics, 50, 1694 (2012)

Calculating mechanics of polymer networks, blends

and copolymers

Macromolecules, in review

J. Pol. Science B: Pol. Physics, 48, 15 (2010)

Morphology of copolymers

Soft Matter, 7, 7539 (2011)

J. Pol. Science B: Pol. Physics, 49, 1479 (2011)

Langmuir, 27, 7836 (2011)

State of the art in

semiempirical force-fields (MEDEA)

Mean absolute errors 0.23% and 0.28% for n-alkane densities and heats of vaporization of n-alkanes at 298 K

C5H12

Method kcal/mol

COMPASS -2.44

M06-2X/6-311++G** -2.38

M06-2X/6-311G** -2.39

M05-2X/6-311++G** -1.87

BLYP/6-311G** -0.03

PBE1PBE/6-311G** -0.43

CAM-B3LYP/6-311G** -0.13

B97D/6-311G** -2.74

SVWN5/6-311G** -3.83

PBEPBE/6-311G** -0.58

Polymeric materials at high strain rates

• PMMA (Plexiglas): Transparent glassy polymer

• Moderate strength and ductility under typical loading conditions

• At high rate loading (15,000 in/s) PMMA transforms into a high-strength-to-density material with a brittle-like nature. The strength-to-density ratio is in excess of high strength steels and titanium alloy

• Fractured cone is generated at the strike point of a high-speed projectile. The cone impedes the projectile’s progress.

increasing

rate

strain

str

ess

“The Fascinating Behaviors of Ordinary Materials under Dynamic Conditions

Emerging Class of Materials for Armor and Blast Protection” (AMMTIAC, 2009)

Shaped

charge jet

<30,000 ft/s

for 10-30 ns

Hertzian

fracture

“Highly nonlinear behavior

of the nano-time materials,

stress wave propagation

may have to be considered

at a very small

molecular unit level.”

Bullet trapped in

Polyurea (PU) coating

Sealed/Healed area

after transit of bullet

• PU: rubbery material

• At high rate of loading and confinement, PU exhibits multi-fold increase in yield and modulus while retaining high elongation properties.

• At extremely high rate, the polymer can flow , healing the bullet hole

Resistance to rupture from different-thickness polyurea coated steel panels

Why Poly(urethane urea)s ?

4,4’-dicyclohexylmethane

diisocyanate Poly(tetramethylene

oxide) Phase

Mixed

Microphase

Separated

Complex Morphology

(S)oft (H)ard

aromatic or aliphatic?

Binding Energy between the hard segments, Compare aromatic with aliphatic version !

Reasons aliphatic instead of aromatic diisocyanate goups are used:

The motivation for using HMDI includes its ultra-violet (UV) radiation stability characteristic desired for

long-term outdoor durability performance, and additionally to explore potential energy dissipation as

result of the deformation associated with the “boat-chair-boat” conformation in HMDI.

QM results (DFT M05 )

Monodentate

urethane-urethane

linkages

Bidentate

urea-urea

linkages

Bidentate

urea-urethane

linkages

Types of hydrogen bonding in

segmented poly(urethane urea)

-10.3

(weakest)

-14.2

(strongest)

-13.0

(intermediate)

Hydrogen bonding in PUU T.L Chantawansri, Y.R. Sliozberg, J.W. Andzelm, A.J. Hsieh,

Polymer, 53(20), 4512 (2012)

aromatic or aliphatic?

DFT Optimization of hard segments of PUU

Lower binding energy

by ~4 kcal/mol

M062X/6-31G** OPT

Conformational search

from over 50 replicas

Aliphatic > aromatic

Flexible chains win!

PS

PC

Glassy polymers are present in e.g.

transparent armor or structural polymer

fibers.

Capability to predict a response of

polymer to external pressure as shown in EOS

critically impacts design of polymers for armor

applications.

dynamics (MD) with LAMMPS program using

~104 atoms models and DFT with CP2K

program using ~103 atoms were used

These results are being used to develop

constitutive models for macroscale simulations

PMMA can defeat shaped

charge jet transforming into

material stronger than steel

PMMA Polymers under isotropic

compression contract and begin to

fracture at P > 30 GPa

Polymer chains under pressure form

strong bonds and become 3D-solids

Fracture of polymers with rings and

semicrystalline is difficult to model with

MD or DFT

We can model fracture of PMMA

polymer, important for transparent armor,

up to 80GPa!

Hugoniot Equation of States (EOS)

for glassy polymers

Amorphous

Atomistic

Models;

MD annealing

DFT with CP2K

DFT Functional ?

Orbital Basis Set ?

Plane wave cutoff ?

NVT, NPT protocol ?

Restricted vs. Unrestricted DFT ?

MS step size ?

System size (KPoints)?

Testing density of PS

BLYP or PBE with DCACP, or Grimme, never GGA

DZVP/DZV is good; TZVP/DZVP not necessary

Plane Wave cutoff 300 Ry

Restricted DFT, MD step 0.5 fs

No KPoints

10

12

14

16

1 501 1001 1501 2001

500

600

700

800

1 501 1001 1501 2001 -1607.6

-1607.4

-1607.2

-1607 1 501 1001 1501 2001

Issues:

o Time of simulations 4ps

o Number of replicas

o Chain length of 4 monomers each

o Unit cell size, up to 1500 atoms

Energy Temperature Pressure

Sensitivity of Hugoniot Calculation

Failure of Grimme model

Property/polymer 1.0 0.9 0.8 0.7

density P(Gpa)

PE a exp 0.85

DCACP 0.82 0.3 1.9 5.5

Grimme 0.89 1.2 4.8 10.8

PEc exp 1.01

DCACP 1.06 5.0 9.5 19.7

Grimme 1.05 6.7

PS exp 1.05

DCACP 1.02 1.0 2.5 7.3

Grimme 1.05 1.3 6.2

PMMA exp 1.18

DCACP 1.08 0.1 2.1 6.2

Grimme 1.17 2.1 6.9 16.2

UNCLASSIFIED

PS PC

Hugoniot Curves

PMMA

PS PMMA

Failure for polymers with rings at 25 Gpa

Accuracy of ReaxFF depends on polymer type

DFT seems to be very good

for PMMA

Andzelm, Chantawansri, Sirk, Byrd, Rice, DYFP 2012, Chem. Phys, 137, 204901, (2012)

0

4

0 2 4 6

0

4

0 2 4 6

0

4

0 2 4 6

CH

CO

OH

Fracture in PMMA

T(K): 3356 1994 816 451 352

RDF

0 Gpa

76 GPa

Optical properties of Peg-Phthalocyanine

Need to calculate excited states:

Color: singlet-singlet

Laser: triplet-triplet

Spectra do not depend on the conformation

and the size of PEG polymer

B and RSA bands: B3LYP/6311G**

Q band: ZINDO(10)/INDO2//DFT

Method\Excited state Q B R

Experiment 677 354 495

DFT:B3LYP/6311G* 637 338 487

ZINDO(10)//DFT 671 317

0

1

400 500 600 700

H → L

H → L+1 H-9 → L (β)

H → L+5 (α)

Mechanism of

UV-Vis and RSA

excitations

Andzelm, Rawlett, Orlicki, Snyder, Baldridge, J. Chem. Theory Comput. 3 (2007) 870

Results for conformations of SiPC-PEG (x=75,250) complexes

System\Excited state Q B R

DFT

1 SiPC-PEG75 633(0.37) 335(0.54) 479(0.31)

2 SiPC-PEG75 633(0.36) 337(0.68) 477(0.22)

1 SiPC-PEG250 631(0.35) 337(0.47) 485(0.25)

2 SiPC-PEG250 631(0.34) 338(0.42) 500(0.18)

Solvent red-shifts spectra by ~20nm

Color of Peg-Phthalocyanine different

than green is due to structure defects

0

1

400 500 600 700

0

1

400 500 600 700

0

1

400 500 600 700

0

1

400 500 600 700

0

1

400 500 600 700

0

1

400 500 600 700

Color green is predicted

Design of Optimal Chromophores

Push-Pull chromophores should have

large NLO (hyperpolarizability, β) and transparency in visible

Conjugated bridge

Donor Acceptor

Challenge to consider atomistic scale:

Two chromophores differ

only in conformations, but β

is vastly different, by 80%

Push-pull chromophore:

Challenge to address dilemma:

Chromophores NLO Transparency

Large high poor

Small low good

Tasks for computations:

• Calculate accurately color (transparency)

• Efficient search at atomistic scale for chromophores with the large β

Specific Army Need: Chromophores

that do not absorb yellow light

n

)(1

)(11

rerfcr

rerfrr

Electron Repulsion = Long-range + Short-range

= Attenuation parameter

Long-range Exact exchange

Short-range Traditional DFT

BNL = DFT-LC approach

Long-range Corrected (LC) Functionals

Baer, Neuhauser, Livshits (BNL); Phys. Rev. Lett. 94 (2005) 043002

Savin (1996).

Ikura, Tsuneda, Yanai, Hirao (2001)

Yanai, Tew, Handy (2004)

Henderson, Izmaylov, Scuseria, Savin, J. Chem. Phys. 127 (2007) 221103

Jacquemin et al., J.Chem. Theory, Comput, 4 (2008) 123

DFT-LC: BNL cancels SIC at the long range

)(|)|,(|)|,( nwnnnn x

lyp

cc

)()()( nnn cxxc

2

3)1)(2(1

12

2)(

2

1

22 qf

x eqq

erfq

qk

n

Density

fkq

Local Fermi vector

0 DFT-like; HF-like

w, Optimized for thermochemistry of G2

Savin term:

Andzelm, Rinderspacher, Rawlett, Dougherty, Baer, Govind, J. Chem. Theory Comput. 5 (2009) 2835

NWChem: BNL Implementation

2-Electron Integrals

Long-range Correction

- Dependent Exchange Full Coulomb (no attenuation)

Attenuated 4-center integrals Dunlap Charge Density Fitting

( 3-center integrals)

)(1

)(11

rerfcr

rerfrr

• NWChem is part of the Molecular Science Software Suite, developed at Environmental

Molecular Sciences Laboratory, a DOE BER user facility, located at PNNL

• Designed and developed to be a highly efficient and portable Massively Parallel

computational chemistry package

• Provides computational chemistry solutions that are scalable with respect to chemical

system size as well as MPP hardware size

Linear response TDDFT in Tamm-Dancoff approximation: AX = ωX

COSMO solvation model

Scales well up to 128 processors

(not dedicated run)

twist ΔE Beta λmax

kcal/mol 10-30 esu nm

exp: 24 380

0 0 106 384

30 0.3 93 381

45 0.7 78 378

60 1.1 58 373

75 1.4 42 300

90 1.5 34 302

HOMO → LUMO

(charge transfer)

380 nm

HOMO-1 → LUMO

HOMO → LUMO+1

π→π*

263 nm

HOMO-1 LUMO+1

Effect of rotation

Free rotation along two single bonds

Rotomers lower λmax, μ and β

CT

π

Effect of association

Failure of

standard DFT for

intermolecular

intractions

Stacking effect:

μ and β → 0

λmax unchanged

Rotation and association of tolanes

MP2,M05

B3LYP

UNCLASSIFIED

H-bonded self-assembly of tolanes

Amido-ester H-bonding in tolanes leads to ~planar structures with

high-rotation barrier, good hyperpolarizability and excellent neutral colorimetry

H-bonds inTolane: Synthesis of New EO-chromophore inspired by Inverse design

OMe

N

NO2

OMe

O

H

Me

O

HN

O

Me

NO2

I

OMe

OMe

O+ DIPA, CuBr, PPh3

Pd(OAc)2, THFReflux

• Complex synthesis with

Pd catalyst

• Experimental UV-Vis

absorption peak at 377 nm

• Hydrogen bond results in

planar structure and

increased “push-pull” effect.

• NMR evidence of

Hydrogen bond (amide

proton heavily deshielded)

Experiment fully confirms computational conformational analysis:

dE: 0.0 4.6 11.1 19.3 UV: 370(0.94),310(0.20) 372(0.89), 309(0.16) 359(0.86),307(0.26) 351(0.68), 310(0.19)

dE: difference in energy (kcal/mol) UV: spectrum in nm (oscillator strength)

Lowest energy

conformer; planar

with the main UV-Vis

peak at 370 nm vs.

377 experiment

377

nm

θ

UNCLASSIFIED

Passivation of Semiconductor surfaces

Ga2O3(100)

Semiconductor oxide

polymer

DFT for optical and transport properties

• transparent armor, NLO-materials

• band gaps, I-V curves

• electron transport

UNCLASSIFIED

Summary

Accurate dispersion forces are necessary for structures of

polymer fragments

Dispersion is vital to study Soldier’s protective clothing,

personnel armor certification

Dispersion may not be essential to study ballistic impact at

compression, but it is necessary for tension

Hydrogen bonding is critically important for structural and

protective polymer materials

“Multifunctional” DFT is needed: good for excited states, band

gaps, optical properties and also for structures

Validation tests should include internal hydrogen bonds and

multiple hydrogen bonds

We need a big DFT (order N) with energy, gradients for at

least 50K atoms