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Quantization of the dipole moment and of the end charges in push-pull polymers

J. Chem. Phys. 127, 194902 (2007); doi:10.1063/1.2799514

Published 15 November 2007

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Konstantin N. Kudin and Roberto Car
Department of Chemistry and Princeton Institute for Science, and Technology of Materials (PRISM), Princeton University, Princeton, New Jersey 08544, USA

Raffaele Resta
CNR-INFM DEMOCRITOS National Simulation Center, Via Beirut 2, I-34014 Trieste, Italy and Dipartimento di Fisica Teorica, Università di Trieste, Strada Costiera 11, I-34014 Trieste, Italy
A theorem for end-charge quantization in quasi-one-dimensional stereoregular chains is formulated and proved. It is a direct analog of the well-known theorem for surface charges in physics. The theorem states the following: (1) Regardless of the end groups, in stereoregular oligomers with a centrosymmetric bulk, the end charges can only be a multiple of 1/2 and the longitudinal dipole moment per monomer p can only be a multiple of 1/2 times the unit length a in the limit of long chains. (2) In oligomers with a noncentrosymmetric bulk, the end charges can assume any value set by the nature of the bulk. Nonetheless, by modifying the end groups, one can only change the end charge by an integer and the dipole moment p by an integer multiple of the unit length a. (3) When the entire bulk part of the system is modified, the end charges may change in an arbitrary way; however, if upon such a modification the system remains centrosymmetric, the end charges can only change by multiples of 1/2 as a direct consequence of (1). The above statements imply that—in all cases—the end charges are uniquely determined, modulo an integer, by a property of the bulk alone. The theorem's origin is a robust topological phenomenon related to the Berry phase. The effects of the quantization are first demonstrated in toy LiF chains and then in a series of trans-polyacetylene oligomers with neutral and charge-transfer end groups. ©2007 American Institute of Physics
History: Received 18 June 2007; accepted 24 September 2007; published 15 November 2007
Permalink: http://link.aip.org/link/?JCPSA6/127/194902/1
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KEYWORDS and PACS

Keywords
PACS
  • 36.20.Fz
    Macromolecular constitution (chains and sequences)
  • 36.20.Ey
    Macromolecular conformation (statistics and dynamics)
  • 33.15.Kr
    Molecular electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility
  • YEAR: 2007

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
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