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6/3/2008
1
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)
6/3/2008
2
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)
6/3/2008
3
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
6/3/2008
4
torsional
intermolecularinteractions
intramolecularnonbonded
bond stretch
valence anglebend
Force fieldsIntramolecular and Intermolecular Interactions
ij
ji
ij
ij
ijij
N
ji
ij
POLNB
r
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
6/3/2008
5
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
6/3/2008
6
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)
6/3/2008
7
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
6/3/2008
8
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
6/3/2008
9
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?
6/3/2008
10
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
6/3/2008
11
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
6/3/2008
12
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?
6/3/2008
13
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
6/3/2008
14