Anomalous Effective Charges in bPolyvinylidene fluoride

1
Anomalous Effective Charges inb-Poly(vinylidene
fluoride)
Nicholas J. Ramer Department of Chemistry Long
Island University C. W. Post Campus
Atomistic Modeling And Simulation
Seminar Massachusetts Institute of
Technology Department of Materials Science and
Engineering May 3, 2006
2
Ferroelectricity
Property of a pyroelectric material to possess a
spontaneous polarization (P) that can be altered
by externally-applied electric field (hysteresis)

• First discovered in Rochelle salt in 1920
• Found to exist in BaTiO3 in 1945
• Poly(vinylidene fluoride) was reported to be
  ferroelectric in 1971

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Some Applications of PVDF
Clamp-on transducer for diesel injection lines
(PVDF co-polymer)
Hydrophones (PVDF has similar acoustic impedance
to water)
Non-volatile memory (oxide/ PVDF co-polymer
composites)
Ducharme S et al. IEEE Trans Dev Mater Rel
20055720.
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Poly(vinylidene fluoride)

• Possesses piezoelectric and pyroelectric
  behavior
• Low dielectric constant and low elastic
  stiffness
• Desirable physical properties (flexibility, low
  density and ease of fabrication)
• Co-polymers possess enhanced properties

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PVDF Structures
Polarization in a-PVDF alternates due to chain
conformation t trans (180) g
gauche (60) Non-polar structure
Polarization in b-PVDF is oriented in same
direction Polar structure
What about chain packing?
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Phases of PVDF
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Structure of b-PVDF

• Planar-zigzag and alternatively-deflected
  molecular structures have been proposed

Can theory shed light on this question?
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Methodology

• Density Functional Theory
• with PBE GGA (U Penn code)
• Norm-conserving non-local pseudopotentials
  (OPIUM code)
• 4 4 4 Monkhorst-Pack k-point mesh
• Periodic boundary conditions using
  experimentally-determined lattice constants
• Hellmann-Feynman Forces

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Structure Determination

• Alternatively-deflected structure is
• 0.018 eV/formula unit higher in energy than
  planar-zigzag
• Thermal motions at experimental temperature (150
  K) may be responsible for better fit of X-ray
  data
• Relaxed alternatively-deflected structure has
  s3 (compared to 7)

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Planar-zigzag Structure
a Lando JB, et al. J Polym Sci Part A-1
19664941. b Hasegawa R, et al. Polym J
19723600.
DFT reproduces experimental structure VERY
WELL! Can DFT give P?
 
 
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Which Polarization?
X
Isolated non-interacting dipoles
(Clausius-Mossotti limit)
X
Since the charge density is continuous in a real
system, the polarization is multi-valued and its
absolute value cannot be computed.
Can we use DFT with PW basis to our advantage?
Pgt0
Plt0
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Berry Phase Method
Integral is closed-path geometric phase or Berry
phase and is defined modulo 2p.
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Polarization in b-PVDF
a Nakhmanson SM et al. Phys Rev Lett
200492115504 and references therein.
DFT results represent upper-limit for P (100
b-phase). But what is happening at atomic level?
ATOMIC CHARGES!
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Types of Atomic Charges
STATIC
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Static Atomic Charges for BaTiO3
Ghosez P et al. Phys Rev B 1998586224 and
references therein.

• Static charges do not give quantitative
  information
• for delocalized electron densities.
• Can provide qualitative description of charge
• transfer from one atom to another.

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Types of Atomic Charges
STATIC
DYNAMIC
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Dynamic Atomic Charges
Dynamic charge is change in polarization with
respect to atomic displacement.
Boundary condition fixing E
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Anomalous Dynamic Atomic Charges
Toy problem Heteronuclear diatomic with dipole
p and bond length r
Static Charge
Dynamic Term
Nominal Charge
Predicts Z(r) can be different than Z(r)
ANOMALOUS
Predicts that Z(r) can be different than Z(r0)
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Dynamic Born Effective Charges in BaTiO3
Ghosez P et al. Phys Rev B 1998586224 and
references therein.
First-principles methods can accurately describe
experimentally-determined effective
charges. BUTare there anomalous charges in
b-PVDF?
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Dynamic Born Effective Charges in b-PVDF
Finite difference of polarizations
a Karasawa N et al. Macromolecules 1992257268.
Z are different from Z and Z(r0) in b-PVDF.
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Atomic Origin of Hysteresis
Ratio of infrared intensity of CF2 bending (or
scissoring) mode correlates with change in
dielectric constant (e) and P.
Can DFT methods describe the atomic motions for
b-PVDF? Vibrational Modes!
Reprinted from Lovinger A Science 19832201115.
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Vibrational Spectra of b-PVDF
Hartree-Fock
Experiment
0 500 1000
1500 2000 2500
3000 3500 Wavenumber (cm-1)
Reprinted from Li JC et al. Appl Phys Lett
2002812223.
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Methodology

• Density Functional Theory
• with PBE GGA (ABINIT code)
• Norm-conserving non-local pseudopotentials
  (OPIUM code)
• 4 4 4 Monkhorst-Pack k-point mesh
• Periodic boundary conditions
• Full relaxation of atomic positions and lattice
  constant
• Perturbation theory (atomic displacements and
  homogeneous electric field)

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Vibrational Spectra of b-PVDF
Hartree-Fock
Experiment
0 500 1000
1500 2000 2500
3000 3500 Wavenumber (cm-1)
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Comparison of Vibrational Frequencies
a Tashiro K, et al. Macromolecules 1985182600.
DFT with GGA agrees extremely well with
experiment.
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Origin of LO-TO Splitting

• Transition dipole caused by atomic vibrations
  generates a macroscopic electric field that
  couples to the LO modes of the polar phonons (q
  M)
• LO mode is shifted to higher frequency than the
  TO mode (q M)
• Quantifies long-range dipole-dipole interactions
  which play role in physical properties and
  ferroelectric phase transition

Can DFT methods describe these experimental
results?
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LO-TO Splitting in b-PVDF
a Tashiro K, et al. Macromolecules 1985182600.
DFT with periodicity accurately describes LO-TO
splitting.
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Conclusions

• Confirm planar-zigzag structure for b-PVDF
• Anomalous effective charges are present in b-PVDF
  (just like other ferroelectric materials)
• DFT yields accurate picture of vibrational
  properties including LO-TO splittings
• Better understanding of atomic origins of
  ferroelectricity in PVDF will aid in design of
  new materials (co-polymers and composites)

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Acknowledgements

• Kimberly Stiso and
• Clifford Raynor
• Research Committee of C. W. Post
• Rappe Group