6/3/2008

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Molecular Dynamics Simulations and Neutron Scattering:

Polymer Melt and Solution Dynamics

Grant D. SmithDepartment of Materials Science and Engineering

University of Utah

Polymer Dynamics and Relaxation

Richard H. Boyd and Grant D. Smith

Cambridge University Press (2007)

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Bill Gate’s Opinion

the act of deceiving deception, dissembling, deceit

misrepresentation, falsification - a willful perversion of facts

fakery - the act of faking (or the product of faking)

indirection - deceitful action that is not straightforward

MD simulation = dissimulation

Outline

� Molecular Dynamics Simulations

� Force Fields and Force Field Parametrization

� MD Simulations and Neutrons: The Connection

� Local Melt Dynamics: Polyethylene

� Local Solution Dynamics: PEO/water Solutions

� Chain Dynamics: Poly(butadiene)

� Glass and Sub-glass Processes: Poly(butadiene)

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MD Background:Scales of Modeling

Ηψ = Εψ

quantumchemistry

F = MA

moleculardynamics

exp [-∆E/kT]

Monte Carlo

domain

mesoscalecontinuum

Length Scale

Tim

e Sc

ale

10-10

M 10-8

M 10-6

M 10-4

M

10-12

S

10-8

S

10-6

S

10-4

S

MD Background: Classical Equations of MotionNVE

H = K + V = total energy = constant

K= ∑i

iivm2

21

, V = ∑ji

ijrU,

)(

drjdt =

∂H∂pj = vj ,

dpjdt = -

∂H∂rj =-

∂V∂rj = Fj

NVT

H = K + V + Ks + Vs = constant

Ks = ½ Qps2

Vs = (f + 1)kBT ln(s)

ps = conjugate momentum of thermostatQ = conjugate masss = generalized coordinate of the thermostatf = number of degrees of freedom

5000 atoms, 4 nm

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torsional

intermolecularinteractions

intramolecularnonbonded

bond stretch

valence anglebend

Force fieldsIntramolecular and Intermolecular Interactions

ij

ji

ij

ij

ijij

N

ji

ij

POLNB

r

qq

r

CrBArVrV

06

1, 4)exp(

21

)()(πε

+−−+= ∑=

rr

−

=−=−

612

6124)(

ijijij

ij

ij

ij

ij

REPDIS

rrr

C

r

ArV

σσε

)()()()()( ijkl

dihedrals

TORS

ijk

bends

BEND

ij

bonds

BONDNBVVrVrVrV ϕθ ∑∑∑ +++=

rr

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Force fields: Where do they come from?

“Generic” (e.g., Dreiding):

Roughly describe a wide range of materials, not

parameterized or validated

“ Trained” (e.g., AMBER, COMPASS, CHARMM, OPLS)

Parameterized to reproduce the properties of a broad set of

molecules such as small organics, peptides or amino acids

“Specialized” (e.g., Atomistic Polarizable Potential for

Liquids, Electrolytes and Polymers (APPLE&P))

Carefully parameterized and validated potentials designed to

reproduce properties of a small class of specific molecules

r(C-OW) (Å)3 4 5 6

bind

ing

(kca

l/mol

)

-6

-3

0

3 quantum chemistryforce field

hydrophilic path

hydrophobic path

Force Field Parametrization: Intermolecular Interactions

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φ2, degrees

0 40 80 120 160

∆E

(kc

al/m

ol)

0

2

4

6t-φ

2-t, force field

t-φ2-t, quantum chemistry

Force Field Parametrization: Intramolecular Interactions

β dihedral angle

0 60 120 180 240 300 360

conf

orm

atio

nal e

nerg

y (k

cal/m

ol)

0

1

2

3

4

5

6

7QCFF

CH

HC

H2

C

CH2

CH

CH

H2

CH2

C

CHHC

CH2

CH2

Poly(butadiene)

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q, Å -11 2 3 4 5 6 7 8 9 10

S(q)

-1

-0.5

0.0

0.5

1.0Neutron Diffraction MD

Force Field Parametrization: Validation: Static Structure Factor

22

2

)0()0(

)0()0()()(

θθ

θθθ

−

−=

ttTACF

Force Field Parametrization: Validation: Time Correlation Functions

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time (ps)

0 50 100 150 200 250

I(q,

t)

0.001

0.01

0.1

1QENS, q=0.718 Å -1

QENS, q=0.913Å -1

QENS, q=1.095 Å -1

Incoherent Dynamic Structure Factor,

QENS and MDCoherent Dynamic Structure Factor,

NSE and MD

Force Field Parametrization: Validation: Dynamic Structure Factor for PEO Melt

Simulation yields intermediate dynamic structure factors (time domain) directly

Coherent scattering

Incoherent scattering

� Simulation time scales from femtoseconds to microseconds

� Experimental time scales from picoseconds to nanoseconds

� A Fourier-Laplace to frequency domain (or an inverse transform of QENS data) is required for comparison

� Direct comparisons can be made with NSE data

MD-Neutron Connection: Dynamic Structure Factors

>−−>=<−•<= ∑∑ |)0()(|/|)0()(|sin))0()((exp1

),(,,

jk

N

kj

jk

N

kj

jkcoh rtrqrtrqrtrqiN

tqsrrrr

∑∑ >−−=<>−•<=N

k

kkkk

N

k

kkinc rtrqrtrqrtrqiN

tqs |)0()(|/|)0()(|sin))0()((exp1

),(rrrrrrr

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Example: Local Dynamics is a Polyethylene Melt:

MD simulations provide data over a wider range of timeMD simulations are in good agreement with QENS

>∆<−=

6

)(exp),(

22 trqtqs H

inc

Librations or Conformational Transitions?

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PEO/Water Solutions: Local DynamicsPolymer Dynamics

q = 0.4 A-1

q = 2.4 A-1

Mw = 500

wP

0.0 0.2 0.4 0.6 0.8 1.0

time

(ps)

0.1

1

10

100

1000

10000 τDSF(q=0.58 Å-1 )

τDSF(q=0.91 Å-1)

τDSF(q=1.57 Å-1)

wP

0.0 0.2 0.4 0.6 0.8 1.0

tim

e (p

s)

101

102τTRANS(C-C)

τTRANS(C-O)

τ2(CH vector)

Low molecular weight

PEO exhibits a

minimum in local

dynamics with

concentration

This is due to slowing

conformational

dynamics and

increasing

translational/rotational

dynamics with dilution

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time (ps)

0 10 20 30

I(q,

t)

0.0

0.2

0.4

0.6

0.8

1.0

q=0.57 Å -1

q=0.90 Å -1

q=1.62 Å -1

q=2.24 Å -1

wP=0.53, 298 K

PEO/Water Solutions: Local DynamicsWater Dynamics

Water quasi-confinement

q2, Å-2

0 1 2 3 4 5

Γ (

ps-1

)

0.0

0.5

1.0

wP=0.17, qc=0.95 Å-1

wP=0.52, qc=1.34 Å-1

wP=0.78, qc=1.58 Å-1

separation (Å)

2 4 6 8 10

g O-O

(r)

0.0

0.5

1.0

wP=0.17

wP=0.52

wP=0.78

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Large Scale Dynamics: Single chain coherent dynamic structure factor for PBD (353 K)

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20

S'(q

,t)

time (ns)

q = 0.30

q = 0.05

Å-1

Å-1

q = 0.08 Å-1

q = 0.10 Å-1

q = 0.14 Å-1

q = 0.24 Å-1

q = 0.20 Å-1

S'(q,t) = S(q,t)/S(q) = ∑(m,n)

<sin[qRmn(t)]/qRmn(t)> / ∑(m,n)

<sin[qRmn(0)]/qRmn(0)>

CH

HC

H2

C

CH2

CH

CH

H2

CH2

C

CHHC

CH2

CH2

Why does the Rouse model provide such

a poor description of S(q,t)?

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10

S'(q

,t)

time (ns)

Figure 5

Chain stiffness?

Internal viscosity?

Non-Gaussian

displacements?

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1000/T

3 4 5 6 7 8

log (

1/τ

) (

s-1

)

-4

-2

0

2

4

6

8

10

Ts T

g

β

α

α−β

dielectric relaxation

Can dynamic neutron scattering tell us

about the bifurcation of the glass and sub-

glass processes?

MD Simulations and Dynamic Neutron

Scattering in Polymers

--Natural partners (overlapping time and length scales)

--DNS experiments are important for validation of

simulations

--Simulations can direct experiment

--Simulations can help provide mechanistic insight into

experimental results

--Simulations can help provide sanity checks for

conclusions based on limited (but expanding!) DNS

capabilities

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