I. Polyvinylidene fluoride (PVDF) and its relatives

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Serge Nakhmanson
Self-polarization in ferroelectric polymers
I. Polyvinylidene fluoride (PVDF) and its
relatives a brief reminder II.
Polarization via maximally-localized Wannier
functions and why it is so good to study
polymers a brief reminder III. Projects a.
Self-polarization in individual polymer (and
copolymer) chains b. Self-polarization in PVDF
from a chain to a crystal c. Self-polarization in
PVDF/copolymer crystals IV. Conclusions
Collaborators Jerry Bernholc and Marco
Buongiorno Nardelli (NC State and ORNL)
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The nature of polarization in PVDF and its
relatives
Representatives polyvinylidene fluoride (PVDF),
PVDF copolymers, odd
nylons, polyurea, etc.
PVDF copolymers
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Growth and manufacturing
Pictures from A. J. Lovinger, Science 1983
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Growth and manufacturing
Pictures from A. J. Lovinger, Science 1983
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Growth and manufacturing
PVDF grown approx. 50 crystalline, which
spoils its polar properties

• PVDF copolymers (with TrFE and TeFE)
• can be grown very (90-100) crystalline
• can be grown as thin films
• stay ferroelectric in films only a few Å thick

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What is available? Simple models for polarization
in PVDF
Experimental polarization for approx. 50
crystalline samples 0.05-0.076
C/m2 Empirical models (100 crystalline)
Polarization
(C/m2) Rigid dipoles (no dipole-dipole
interaction)
0.131 Mopsik and Broadhurst, JAP, 1975
Kakutani, J Polym Sci, 1970 0.22
Tashiro et al. Macromolecules 1980

0.140 Purvis and Taylor, PRB 1982, JAP 1983

0.086 Al-Jishi and Taylor, JAP 1985

0.127 Carbeck, Lacks and Rutledge, J Chem Phys,
1995 0.182
Nobody knows what these structural-unit dipoles
are and how they change
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ß-phase layout
Orthorhombic cell for ß-PVDF

• We will consider
• Chains 4 x unit or 8 x unit
• Crystalline systems
• 4 x chain with 4 units
• orthorhombic box 10x10x10 Å

Berry phase method with DFT/GGA P3 0.178 C/m2
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Polarization in polymers with Wannier functions

• Electronic polarization looks especially simple
  when using Wannier functions

• Ionic polarization is also a simple sum

• Unlike in a typical Berry-phase calculation, we
  can attach a dipole moment
• to every structural unit

• Unlike in a typical Born-effective-charge
  calculation for perovskite-type
• materials (e.g., layer-by-layer
  polarization), our analysis will be precise

• We use the simultaneous diagonalization
  algorithm at G-point to compute
• maximally-localized Wannier functions within
  our real-space multigrid method
• (GGA with non-local, norm-conserving
  pseudopotentials)
• See previous Serges talk for details
• See also Gygi, Fattebert, Schwegler, Comp. Phys.
  Commun. 2003
• See E. L. Briggs, D. J. Sullivan and J.
  Bernholc, PRB 1996 for the multigrid method
  description

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Example Wannier functions in a ß-PVDF chain
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Example Wannier functions in a ß-PVDF chain
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Structural-unit dipole moments in individual
chains
A dipole moment of a structural unit in a chain
gives us a good natural starting value for a
dipole moment of a particular monomer
VDF
TrFE
TeFE
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Playing lego with structural units in a chain
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Playing lego with structural units in a chain
TeFE
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Playing lego with structural units in a chain
HTTH defect
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Playing lego with structural units in a chain
CHF-CHF
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• Some general observations for chains
• All kinds of interesting structural-unit dipole
  arrangements along
• a chain are possible (experimentalists can
  not yet synthesize
• polymers with such precision, though)
• Structural-unit dipoles on a chain like to keep
  their identities,
• i.e., they stay close to their natural
  values and self-polarization
• effects are weak
• Now we start packing chains into a crystal and
  see what happens

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Packing ß-PVDF chains into a crystal
noninteracting chains
weakly interacting chains
crystal
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Now we know why simple models disagree!
Empirical models (100 crystalline)
Polarization (C/m2) Rigid
dipoles (no dipole-dipole interaction)
0.131 Mopsik and
Broadhurst, JAP, 1975 Kakutani, J Polym Sci,
1970 0.22 Tashiro et al.
Macromolecules 1980
0.140 Purvis and
Taylor, PRB 1982, JAP 1983
0.086 Al-Jishi and
Taylor, JAP 1985
0.127 Carbeck,
Lacks and Rutledge, J Chem Phys, 1995
0.182
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On to more complex PVDF/copolymer crystals

• Now when we know what is going on with ß-PVDF
  crystal, lets transform it into
• a PVDF/copolymer crystal by turning some VDF
  units into the copolymer ones
• We will randomly change some VDF units into
  TrFE or TeFE taking
• into account that they dont like to sit
  too close to each other
• Volume relaxations will be important
• Our grid-based method can not do volume
  relaxation, we use PWscf/USPPs
• to get us to the volume that is about right
• Polarization will not be too sensitive to small
  stress variations
• We will monitor structure
• Volume and lattice constants
• Dihedral angles between units
• and polarization
• Dipole moment values in structural units will
  they keep their identities?
• Total polarization
• in our models as we change PVDF/copolymer
  concentration

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This is how a relaxed model looks like

• Example P(VDF/TrFE) 62.5/37.5 model (6 units out
  of 16 changed into TrFE)

Front view
Side view
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This is how a relaxed model looks like

• Example P(VDF/TrFE) 62.5/37.5 model (6 units out
  of 16 changed into TrFE)

Front view
Top view
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Volume relaxation in PVDF/copolymer models
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Volume relaxation in PVDF/copolymer models

• Models expand mostly along 1 direction.
• There is no change along the direction of the
  backbone.
• Unit staggering is to blame?

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Dihedral unit-unit angle change

• Models expand mostly along 1 direction.
• There is no change along the direction of the
  backbone.
• Unit staggering is to blame?

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Dipole-moment change in VDF structural units
ß-PVDF crystal
ß-PVDF chain

• VDF unit dipole moments change a lot when
  substantially diluted with less polar units
• Close to linear drop in unit dipole strength with
  changing concentration

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Dipole-moment change in copolymer structural units
TrFE chain
TeFE chain (nonpolar)

• Copolymer units become strongly polarized when
  surrounded by more polar VDF units
• Copolymer unit polarization decreases with
  concentration but never goes back to its
  natural chain value

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Total polarization in PVDF/copolymer models
ß-PVDF crystal

• Mapped out the whole polarization vs
  concentration curve!
• Linear to weakly parabolic (?) polarization drop
  with concentration
• Considering the estimative character of
  calculations, remarkable agreement with
  experimental data
• Volume relaxation is important no agreement with
  experiment at fixed volume

Tajitsu et al. Jpn. J. Appl. Phys. 1987
Tasaka and Miyata, JAP 1985
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Conclusions

• Better understanding of polar polymers in chains
  and crystals
• The nature of dipole-dipole interaction in polar
  polymer crystals is complex (although, the curves
  are simple)
• Information about the structure and polarization
  in PVDF/copolymer compounds is now available. It
  can be used as a guide to design materials with
  preprogrammed properties.
• We have the models now, so that we can do other
  things with them