1. North Carolina State University Superpolar polymers by design
Serge Nakhmanson
North Carolina State University
Superpolar polymers by design
I. Introduction: A family of ferroelectric polymer materials
II. Methodology: How do we compute polarization in
periodic solids?
III. Polymers dissected:
a. PVDF and its relatives
b. “Superpolar” polymers made from PVDF by
atomic substitution
IV. Conclusions and comparisons to other materials
Acknowledgments:
Collaborators: Discussions:
Jerry Bernholc (NC State) Michel Cote (U. Montreal)
Marco Buongiorno Nardelli (NC State)

2. Introduction

3. Boron-Nitride nanotubes: quasi-1D nano-piezoelectrics
Carbon
Boron-Nitride c
Zigzag nanotube index
All wide zigzag or chiral BN nanotubes are not pyroelectric due to screw symmetry!
But breaking of the screw symmetry by bundling or
deforming BNNTs makes them weakly pyroelectric:
See Nakhmanson et al. PRB 2003

4. The nature of polarization in PVDF and its relatives
Representatives: polyvinylidene fluoride (PVDF), PVDF copolymers,
odd nylons, polyurea, etc.
PVDF copolymers
PVDF structural unit
with trifluoroethylene
P(VDF/TrFE)
with tetrafluoroethylene
P(VDF/TeFE)
Spontaneous polarization:
Piezoelectric const (stress): up to
Mechanical/Environmental properties: light, flexible, non-toxic, cheap to produce
Applications: sensors, transducers, hydrophone probes, sonar equipment
Weaker
than in PZT!

5. Growth and manufacturing
Pictures from A. J. Lovinger, Science 1983

6. Growth and manufacturing
β-PVDF
Pictures from A. J. Lovinger, Science 1983

7. Growth and manufacturing
PVDF: grown approx. 50% crystalline
Copolymers can be grown
80-90% crystalline!
β-PVDF

8. “Dipole summation” models for polarization in PVDF
Experimental polarization for approx. 50% crystalline samples:
Empirical models (100% crystalline) Polarization ( )
Rigid dipoles (no dipole-dipole interaction):
Mopsik and Broadhurst, JAP, 1975; Kakutani, J Polym Sci, 1970:
Tashiro et al. Macromolecules 1980:
Purvis and Taylor, PRB 1982, JAP 1983:
Al-Jishi and Taylor, JAP 1985:
Carbeck, Lacks and Rutledge, J Chem Phys, 1995:
Which model is better? What about copolymers?
Ab Initio calculations can answer these questions

9. Computing polarization

10. Computing polarization in a periodic solid
Modern theory of polarization
R. D. King-Smith & D. Vanderbilt, PRB 1993
R. Resta, RMP 1994
1) Polarization is a multivalued quantity and its absolute value cannot be computed.
2) Polarization derivatives are well defined and can be computed.
Piezoelectric polarization:
Spontaneous polarization:
The scheme to compute polarization with MTP can be easily formulated
in the language of the density functional theory.

11. Some technical details
Massively parallel real-space multigrid method to solve
Kohn-Sham equations
See E. L. Briggs, D. J. Sullivan and J. Bernholc, PRB 1996
Density functional theory with generalized gradient approximation
for the exchange-correlation interaction
Non-local, norm-conserving pseudopotentials in separable form
Berry-phase method for polarization calculations
Accurate Brillouin zone sampling
High energy cutoffs ( Ry)

12. Polarization in ferroelectric polymers

13. Polarization in β-PVDF from the first principles
uniaxially oriented
non-poled PVDF – not polar
β-PVDF – polar
Berry phase method
with DFT/GGA
Carbeck et al. (1995):
No sensible comparison to
experiment because β-PVDF is
only 50% crystalline!

14. Polarization in PVDF copolymers
Copolymers can be grown 80-90% crystalline!
P(VDF/TrFE) 75/25 copolymer
P(VDF/TeFE) 75/25 copolymer
Comparison with experiment:
in 75/25 P(VDF/TrFE) copolymer
projected to 100% crystallinity
(Tajitsu et al. Jpn. J. Appl. Phys. 1987)
(Furukawa, IEEE Trans. 1989)
in 75/25 P(VDF/TeFE) copolymer
(Tasaka and Miyata, JAP 1985)

15. Piezoelectricity in PVDF and copolymers
PVDF/TrFE 75/25
PVDF/TeFE 75/25
-0.268
(-0.130) [1]
(-0.26) [2]
-0.183
-0.135
-0.270
(-0.145) [1]
(-0.09) [2]
-0.192
-0.145
-0.332
(-0.276) [1]
(-0.25) [2]
-0.211
-0.150
[1] Tashiro et al. Macromolecules, 1980
[2] Carbeck and Rutledge, Polymer, 1996

16. PVDF and copolymers: good agreement between our calculations
and the experiments
this proves the validity of our approach for
polymeric substances

17. Backbone substitution in PVDF
polyaminodifluoroborane (PADFB) ?
PVDF
2.1
2.5
Carbon +
2.1
3.0
Nitrogen ++
Pauling
electronegativities
2.5
4.0
Carbon –
2.0
4.0
Boron
– –

18. Backbone substitution in PVDF
polyaminodifluoroborane (PADFB)
PVDF
Question: How large will be the improvement in polarization?
An ab initio calculation will give us a good estimate!
BTW: polyaminoborane (PAB), a BN analogue
of polyethylene should also be polar

19. Polarization in BN-based polymers
β-PVDF
0.178
-0.268
-0.270
-0.332
PADFB
0.362
-0.493
-0.580
-0.555
PAB
0.300
-0.348
-0.398
-0.431
PbTiO3
0.88
-0.93
3.23
PbTiO3 data from
G. Saghi-Szabo et. al. PRL 1998, PRB 1999.
PADFB: polar properties improve by approximately 100%
Additional bonus:
improved thermal stability
Rotation angle

20. Polar materials: the big picture
Representatives
Properties
Lead Zirconate Titanate (PZT) ceramics
Polymers
polyvinylidene fluoride (PVDF),
PVDF copolymers
BN-based polymers
Material
class
Polarization
( )
Piezoelectric const ( )
up to 0.9
5-10
up to 0.2
0.5?
0.35?
Good pyro- and piezoelectric properties
Pros
Weight?
Brittleness?
Toxicity?
Pyro- and piezoelectric properties weaker than in PZT ceramics
Cons
Light,
Flexible,
Non-toxic,
Cheap to produce
BN nanotubes
(5,0)-(13,0) BN nanotubes
Single NT:
Bundle: ?
~0.01
Light,
Flexible; good piezoelectric properties
Expensive?

21. Conclusions Polarization in PVDF family (C/m2) VDF 0.178 PADFB 0.362
PAB
0.300
TrFE
0.128
TeFE
0.104
Polarization in
PVDF family (C/m2)
Quantum mechanical theory of
polarization works well in polymer
materials like β-PVDF and its
copolymers.
Our results for β-PVDF can be
used to calibrate empirical models
for polarization in this polymer
Intuitive models can be combined with first principles calculations of polarization to design “superpolar” polymers:
Excellent mechanical and environmental properties inherited from PVDF
Polar properties up to 100% better than in PVDF
Enhanced thermal stability
Numerous applications: sensors, actuators, transducers
Have been already synthesized, but only as precursors for other materials
A whole zoo of other polar polymers to play with
Preprint available:
S. M. Nakhmanson, M. Buongiorno Nardelli and J. Bernholc, PRL in press (2004)

22. Future projects Empirical model of polarization in PVDF and
copolymers from the Wannier function centers?