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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 relativesb. “Superpolar” polymers made from PVDF by atomic substitution

IV. Conclusions and comparisons to other materials

Superpolar polymers by design

Serge NakhmansonNorth Carolina State University

Acknowledgments:

Collaborators: Discussions:Jerry Bernholc (NC State) Michel Cote (U. Montreal)Marco Buongiorno Nardelli (NC State)

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Introduction

NC STATE UNIVERSITYBoron-Nitride nanotubes: quasi-1D nano-piezoelectrics

c

c Carbon

Boron-Nitride

All wide zigzag or chiral BN nanotubes are not pyroelectric due to screw symmetry!

But breaking of the screw symmetry by bundling ordeforming BNNTs makes them weakly pyroelectric: 2C/m 01.0 tot

zP

Zigzag nanotube index

See Nakhmanson et al. PRB 2003

NC STATE UNIVERSITYThe nature of polarization in PVDF and its relatives

Spontaneous polarization:Piezoelectric const (stress): up to

Mechanical/Environmental properties: light, flexible, non-toxic, cheap to produceApplications: sensors, transducers, hydrophone probes, sonar equipment

2C/m 2.01.0 2C/m 2.0 Weaker

than in PZT!

Representatives: polyvinylidene fluoride (PVDF), PVDF copolymers, odd nylons, polyurea, etc.

PVDF copolymerswith trifluoroethylene

P(VDF/TrFE)

PVDF structural unit with tetrafluoroethyleneP(VDF/TeFE)

NC STATE UNIVERSITYGrowth and manufacturing

Pictures from A. J. Lovinger, Science 1983

NC STATE UNIVERSITYGrowth and manufacturing

Pictures from A. J. Lovinger, Science 1983β-PVDF

NC STATE UNIVERSITYGrowth and manufacturing

β-PVDF

Copolymers can be grown 80-90% crystalline!

PVDF: grown approx. 50% crystalline

NC STATE UNIVERSITY“Dipole summation” models for polarization in PVDF

Experimental polarization for approx. 50% crystalline samples: 0.05-0.076

Empirical models (100% crystalline) Polarization ( )

Rigid dipoles (no dipole-dipole interaction): 0.131Mopsik 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: 0.086Al-Jishi and Taylor, JAP 1985: 0.127Carbeck, Lacks and Rutledge, J Chem Phys, 1995: 0.182

2C/m

2C/m

Which model is better? What about copolymers?Ab Initio calculations can answer these questions

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Computing polarization

NC STATE UNIVERSITYComputing polarization in a periodic solid

2) Polarization derivatives are well defined and can be computed.

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.

Piezoelectric polarization:

)( )0(ii

i i

xxx

PeP

)nonpolar()polar( PPP

Spontaneous polarization:

The scheme to compute polarization with MTP can be easily formulatedin the language of the density functional theory.

NC STATE UNIVERSITYSome 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 (70-100 Ry)

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Polarization in ferroelectric polymers

NC STATE UNIVERSITYPolarization in β-PVDF from the first principles

β-PVDF – polar

No sensible comparison toexperiment because β-PVDF is

only 50% crystalline!

uniaxially oriented non-poled PVDF – not polar

2C/m 178.0PBerry phase method

with DFT/GGA

Carbeck et al. (1995):2C/m 182.0P

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P(VDF/TeFE) 75/25 copolymerP(VDF/TrFE) 75/25 copolymer

Polarization in PVDF copolymers

2C/m 128.0P 2C/m 104.0P

Copolymers can be grown 80-90% crystalline!

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)

2C/m 123.0P

Comparison with experiment: in 75/25 P(VDF/TeFE) copolymer projected to 100% crystallinity

(Tasaka and Miyata, JAP 1985)

2C/m 118.0P

NC STATE UNIVERSITYPiezoelectricity in PVDF and copolymers

PVDF 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

)(C/m231e

)(C/m232e

)(C/m233e

[1] Tashiro et al. Macromolecules, 1980

[2] Carbeck and Rutledge, Polymer, 1996)0(

)0(3

3 ,i

iii

ii x

xxPe

2333 C/m 233 :PbTiO .e

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PVDF and copolymers: good agreement between our calculations

and the experiments this proves the validity of our approach for

polymeric substances

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Paulingelectronegativities

Backbone substitution in PVDF

PVDF

2.1

2.5

2.1

Carbon

+

2.5

4.04.0

Carbon

–

2.12.1

3.0Nitrogen

++

2.0

4.04.0

Boron

– –

polyaminodifluoroborane (PADFB)

?

NC STATE UNIVERSITYBackbone substitution in PVDF

PVDF polyaminodifluoroborane (PADFB)

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

NC STATE UNIVERSITYPolarization 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

)(C/m231e )(C/m2

32e)(C/m23spP )(C/m2

33e 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

NC STATE UNIVERSITYPolar materials: the big picture

RepresentativesProperties

Lead Zirconate Titanate (PZT)

ceramics

Polymers

polyvinylidene fluoride (PVDF),

PVDF copolymersBN-based polymers

Materialclass

3PbTiO

Polarization( )

Piezoelectric const ( )

2C/m 2C/m

up to 0.9 5-10

up to 0.20.5?

0.1-0.20.35?

3x-1x OTiPbZr3PbZrO

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:0.25-0.4Bundle:

?

Single NT:0

Bundle: ~0.01

Light,Flexible; good piezoelectric

properties

Expensive?

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VDF0.178

PADFB0.362

PAB0.300

TrFE0.128

TeFE0.104

Polarization inPVDF family (C/m2)

Conclusions

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)

NC STATE UNIVERSITYFuture projects

Empirical model of polarization in PVDF andcopolymers from the Wannier function centers?