6.10: Polyacetylene (average bond model)

Introduction to Nanoelectronics · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY-NC-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    The carbon backbone of polyacetylene consists of alternating single and double bonds. Thus, there are two possible configurations: single-double-single-double or double-single-double-single.

    Screenshot 2021-05-25 at 16.29.43.png
    Figure \(\PageIndex{1}\): The simplest model for polyacetylene is an average of the two possible alternating single-double bond configurations.

    The simplest model assumes that every carbon atom in polyacetylene is identical. The carbon-carbon bonds are then an average of single and double, and the unit cell is a single carbon atom and its associated hydrogen atom. Under this model, to construct a polyacetylene chain, we should translate the primitive unit cell a distance \(a_{0}\). Thus the primitive lattice vector is \(\bf{\tilde{a_{1}}} = a_{0}\tilde{x}\), where we arbitrarily positioned the chain parallel to the x-axis.

    6.10: Polyacetylene (average bond model) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.