Transcript Document

Modeling Mesoscale Structure In
Comb Polymer Materials for
Anhydrous Proton Transport
Applications
Barry Husowitz
Peter Monson
Why is this important?
 Proton
Exchange Membrane (polyelectrolyte)
 Membranes need to be
 Chemically stable
 Thermodynamically stable
 Reasonable proton conductance
Important for Operation of Fuel Cell (Proton Exchange Membrane)
U.S. Department of Energy Hydrogen Program
Water Assisted Proton Conductance
 Nafion
(comb polymer)
 The conductance of water containing nafion is
highly dependent on the state of hydration of the
membrane and structural characteristics
 Temperature range of operation highly dependent
on solvent
P. J. Brookman, J. W. Nichoson, "Developments in Ionic Polymers, vol
2" Elsevier, London, pp. 269-283 (1986)
Anhydrous proton conductance
 Conductance
does not depend on physical
properties of the solvent
 Investigating proton-conducting polymers
which do not rely on a solvent is a
revolutionary approach to new hydrogen fuel
cells
Center for Chemical Innovations (CCI) : Candidates
for Anhydrous Proton Conductance
Imidazole
N
NH
H
N
N
 Comb
Benzotriazole
N
diblocks
O
Br
Br
m
O
S
O
O
n
S
O
O
O
NH
N
HN
 Comb
polymers
O
O
n
O
N
H
C10H 21
O
O
n
N
H
Center for Chemical Innovations (CCI) : Candidates
for Anhydrous Proton Conductance
N
NH
PT
H
N
N
N
 Dendrimer-Linear
PT
Modeling
Polymer Architecture
(chemistry/structure)
Predict
(model)
What is the correlation
between the nanostructure
and proton conductance?
Mesoscale Structure
(ordering)
Coarse Grained Models
conformational
rearrangements ~ 10-12 - 10-10 s
5
bond
vibrations
~ 10-15 s
diffusion
~ 10-9 -10-6 s
5
Want a coarse-grained model for polymers
3
that captures relevant interactions, excluded
1
4 volumes, repulsion between unlike atoms
2
Number of Atoms
- Using softer potentials and reducing the
Lumped into Effective
degrees of freedom is an efficient technique
Segment (interaction
6 segments)
for
large
dense
systems
(10
center) MC, MD, DPD
F. Muller-Plathe, CHEMPHYSCHEM 3, 754-769 (2002)
Multiscale Modeling: Force Fields
Quantum
Calculations of
energy surface
Quantum
Mechanics
Force Field - Functional
forms and Parameters to
describe the potential
energy of atoms or
groups of atoms
Molecular Mechanics
– Newtonian
mechanics to model
molecular system
Classical
Physics
conformational
rearrangements ~ 10-12 - 10-10 s
5
4
2
1
3
bond
vibrations
~ 10-15 s
H. Sun, Macromolecules 28, 701-712 (1995)
diffusion
~ 10-9 -10-6 s
Basic Model For Polymers
 Minimal
coarse graining model that captures
relevant interactions, connectivity, excluded
volumes
Base Case Model Hamiltonian
H=Hb + Hnb
Bonding interactions within the
chains (Conformational states of
individual polymers), connectivity
Interactions between other
chains and non-bonded sites
Bonding Hamiltonian (Ideal Chain
Models)
 Connectivity
(Molecular Architecture)
 Freely joined chain
 Key Parameter b
 Discrete Gaussian chain
ri(s)
Fixed
b
ri(s+1)
ri(s)
Reo=bN1/2
G. R. Strobl, Chapter 6 "The Physics of Polymers, 2'nd Ed." Springer, NY,
(1997)
ri(s+1)
Non-bonding Hamiltonian
 Essential
Interactions described through simple
parameters, chain extension Reo, Flory-Huggins (
N AB), compressibility (N ), acts like excluded
volume No explicit volume exclusion, segments can
Symmetric Diblock
overlap, enforce low compressibility on
length scale of interest Reo

A,m
Reo
{
L
L {
L=0.17Reo
-1
K. Daoulas and M. Muller, J. Chem. Phys. 125, 184904 (2006)
0
r-rc
1
Metropolis Algorithm For Monte Carlo Simulation
The basic idea is that we assume each configuration of a system has a
probability proportional to a Boltzmann factor or
P(i) = e
-Ei /kT
Consider two configurations A and B, each of which occurs with
probability proportional to the Boltzmann factor. Then
The nice thing about forming the ratio is that it converts relative
probabilities involving an unknown proportionality constant (called
the inverse of the partition function), into a pure number. We can
achieve the relative probability of the last equation in a simulation by
proceeding as follows:
Metropolis Algorithm For Monte Carlo Simulation
1. Start from configuration A, with know energy EA, make a
change in the configuration to obtain a new (nearby)
configuration B.
2. Compute EB (typically a small change from EA, but not to
small)
3. If EB < EA, assume the new configuration , since it has
lower energy (desirable thing, according to the boltzmann
factor).
4. If EB > EA, accept the new (higher energy) configuration
with -(E -E )/T This means that when the temperature is
e
B
A
high, we don’t care if we take a step in the “wrong” direction,
but as the temperature is lowered, we settle into the lowest
configuration we can find in our neighborhood.
Metropolis Algorithm For Monte Carlo Simulation
If we follow these rules, then we will sample points in the space of
all possible configurations with probability proportional to the
Boltzmann factor, consistent with the theory of equilibrium
statistical mechanics. We can compute average properties by
summing them along the path we follow through possible
configurations.
The hardest part about implementing the Metropolis algorithm is
the first step: how to generate “useful” new configurations.
Z = å e-Ei /kT
i
Canonical Partition function – Sum of
all the different possible energy states
of the system (However, maybe one of
these configurations is very very low
in energy and dominates the sum)
Monte Carlo Moves Incorporated
1. Moved single beads in the chain
2. Translated the whole chain
3. Reptation
Simulation Methods
 Single
Chain in Mean Field (SCMF)
 Chains move in a field created by other chains via
model Hamiltonian
 Update the fields periodically based on segment
distribution
 Direct Monte Carlo (MC) simulation of the model
Hamiltonian
 Consider new and old fields for every MC move
 Update fields after every accepted move
Advantage of Model
 Retains
computational advantage of Self-consistent
Field theory (SCF), but includes fluctuations.
 The evaluation of interactions via a grid and
densities speeds up the energy calculation by about
two order of magnitude compared to explicit
pairwise interactions.
 Can easily implement different polymeric
structures (branched polymers, dendrimeric
polymers etc.) or architectures with this model.
Experimental Results: Morphology of Comb
Polymers by X-ray Scattering
q1
q2/q1=3
q2
X-ray scattering clearly reveals nano-scale phasesegregation induced by alkyl chains
Chen et al, Nature Chemistry , 2010, 2, 503-508
Experimental Results: Morphology of Comb
Polymers by X-ray Scattering
q1
q2/q1= 4
q2
X-ray scattering clearly reveals nano-scale phasesegregation induced by alkyl chains
Chen et al, Nature Chemistry , 2010, 2, 503-508
Center for Chemical Innovations (CCI) Comb
Polymers - Coarse Graining
Comparison of SCMF with Previous SelfConsistent Field Theory (SCF) Study of Comb
Polymers
Changing the position of the graft points
and number of branch points provides a
route to a cylinder morphology
Liangshun Zhang et al, J. Phys. Chem. B 2007, 111, 351-357
Monte Carlo simulations of coarse grained model

=
52.2
Experimental
Alkyl side chains gives rise
to cylinder morphology
Our Calculated Structure Factor
q1
q2/q1=
q2
Disordered
structure
in this case
 = 52.2

But, if we lower the interaction parameter
to 40.6 then …
q1
q2/q1= 4
q2
MC simulations of coarse grained model
Alkyl side
chains give
rise to lamellar
morphology
 = 52.2

Experimental
Our Calculated Structure Factor
q1
q2/q1= 4
q2
Disordered
structure
in this case
 = 52.2

But, as before if we lower the interaction parameter
To 40.6 then …
q1
q2/q1= 4
q2
Summary and Conclusions
Coarse grained models of CCI polymers show lamellar,
cylindrical and disordered structures found in experiments
 Simulations may explain origins of disordered structures
seen in some experiments
 Addition of alkyl groups increases value of
required for
ordering in the system (effect of chain branching on orderdisorder transitions)
 Simulations of comb polymer systems for large
starting
from a disordered state can lead to quenched disorder
 Thus simulations of alkylated polymers can show ordered
structures when those of nonalkylated polymers at the
same value of do not

Thank You
 Peter
Monson
 NSF
 Center
for Chemical Innovation
(CCI) at the University of
Massachusetts, Amherst
 Everyone here today