I. Polyvinylidene fluoride (PVDF) and its relatives

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Collective polarization effects in ferroelectric
polymers Serge Nakhmanson (Rutgers), Marco
Buongiorno Nardelli and Jerry Bernholc (NC State
and ORNL)
I. Polyvinylidene fluoride (PVDF) and its
relatives II. Polarization via
maximally-localized Wannier functions and
why it is so good to study polymers III.
Projects a. Self-polarization in PVDF from a
chain to a crystal b. Self-polarization in
PVDF/copolymer crystals IV. Conclusions
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PVDF and its relatives why bother?

• All ferroelectric polymers
• good mechanical/environmental properties
• light, flexible, non-toxic, cheap to produce
• numerous applications sensors, transducers,
• hydrophone probes, sonar equipment

• ß phase of polyvinylidene fluoride (PVDF)
• grown at best 50 crystalline
• polar properties spoiled
• spontaneous polarization 0.1 C/m2

• PVDF copolymers with
• trifluoroethylene (TrFE) and
• tetrafluoroethylene (TeFE)
• grown 90-100 crystalline
• improved polarization
• grown as thin films
• thin films remain ferroelectric

People (experimentalists especially) would like
to learn more about copolymer systems, but not
much theoretical data is available
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Wannier function centers (WFCs) in a ß-PVDF
chain
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
  (monomer)

• Maximally-localized Wannier functions obtained
  with
• simultaneous diagonalization algorithm at
  G-point.
• Use real-space multigrid method (NCSU) to
  solve KS equations.
• GGA with non-local, norm-conserving
  pseudopotentials
• See Gygi, Fattebert, Schwegler, Comp. Phys.
  Commun. 2003
• for the Wannier-function generation algorithm
  description
• See E. L. Briggs, D. J. Sullivan and J.
  Bernholc, PRB 1996
• for the multigrid method description

In a VDF monomer
(1 Debye 3.3410-30 Cm)
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Packing ß-PVDF chains into a crystal
noninteracting chains
weakly interacting chains
crystal
Strong interaction between polymer chains leads
to increased polarization!
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On to more complex PVDF/copolymer crystal models

• Randomly change some VDF units into TrFE or
  TeFE taking
• into account that they dont like to sit
  too close to each other
• Important volume relaxations
• Our grid-based method can not do volume
  relaxation, we use PWscf/USPPs
• to get us to the volume that is about right
• Assume polarization will not be too sensitive to
  small stress variations
• Monitor structure
• Volume and lattice constants
• Dihedral angles between units
• and polarization
• Dipole moment values in structural units
• Total polarization
• in our models with changing PVDF/copolymer
  concentration

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Example this is how a relaxed model looks like

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

Front view
Top view
Notice staggering of the monomers!
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Structural properties of the models

• Observations
• Lattice constant a expands.
• Structural unit staggering is to blame?
• No change along the backbone direction.
• Units stagger differently in models with
• TrFE and TeFE.

Orthorhombic elementary cell with two units
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Polarization in VDF and copolymer structural
units

• Observations
• VDF unit-dipole moments decrease substantially
  when diluted with less polar units
• Copolymer units become strongly polarized when
  surrounded by more polar VDF units
• In both cases nonlinearities in the unit-dipole
  strength with changing concentration

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Total polarization in the models

• Observations
• Mapped out the whole polarization vs
  concentration curve!
• Weakly nonlinear polarization drop with
  concentration
• Considering the estimative character of
  calculations, remarkable agreement with available
  experimental data
• Volume relaxation is important no agreement with
  experiment at fixed volume

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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. Use
  it to design materials with preprogrammed
  properties.
• Models available too!