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)

Introduction

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

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!

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

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

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

“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): 0.131 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 Which model is better? What about copolymers? Ab Initio calculations can answer these questions

Computing polarization

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.

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 (70-100 Ry)

Polarization in ferroelectric polymers

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!

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)

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

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

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 – –

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

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

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? 0.1-0.2 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: 0.25-0.4 Bundle: ? ~0.01 Light, Flexible; good piezoelectric properties Expensive?

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)

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