### Abstract

Van der Waals dispersion forces are examined for an infinite one-dimensional (1D) chain of atoms. Building on the work of Bade and Kirkwood (J. Chem. Phys. 27, 1284, 1957), dipolar fluctuations of the 1D chain are analyzed in terms of polarization waves. The van der Waals energy of the chain is evaluated from the zero-point energy of these waves. Several results are found. (1) A critical value exists for the dimensionless coupling parameter v = α0/a^{3}, for large polarizabilities (α0) or small lattice spacings (a). When v > 0.208, the 1D line has divergences in both the dispersion relation of the waves and the effective site polarizability. The resulting instability is analogous to 1D ferroelectricity. (2) The sum of higher order (than three-body) interactions are shown to be more important than three-body interactions (which are small); when v approaches 0.208, the higher order terms are comparable to the two-body term. (3) Finite 1D chains of N atoms behave like infinite chains when N exceeds 100. (4) 1D surface tensions deviate from two-body predictions for large values of the coupling parameter (v > 0.10).

Original language | English (US) |
---|---|

Pages (from-to) | 1587-1596 |

Number of pages | 10 |

Journal | Molecular Physics |

Volume | 106 |

Issue number | 12-13 |

DOIs | |

State | Published - Jun 1 2008 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Biophysics
- Molecular Biology
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

*Molecular Physics*,

*106*(12-13), 1587-1596. https://doi.org/10.1080/00268970802195066

}

*Molecular Physics*, vol. 106, no. 12-13, pp. 1587-1596. https://doi.org/10.1080/00268970802195066

**Van der Waals energy of a 1-dimensional lattice.** / Cole, Milton Walter; Velegol, Darrell.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Van der Waals energy of a 1-dimensional lattice

AU - Cole, Milton Walter

AU - Velegol, Darrell

PY - 2008/6/1

Y1 - 2008/6/1

N2 - Van der Waals dispersion forces are examined for an infinite one-dimensional (1D) chain of atoms. Building on the work of Bade and Kirkwood (J. Chem. Phys. 27, 1284, 1957), dipolar fluctuations of the 1D chain are analyzed in terms of polarization waves. The van der Waals energy of the chain is evaluated from the zero-point energy of these waves. Several results are found. (1) A critical value exists for the dimensionless coupling parameter v = α0/a3, for large polarizabilities (α0) or small lattice spacings (a). When v > 0.208, the 1D line has divergences in both the dispersion relation of the waves and the effective site polarizability. The resulting instability is analogous to 1D ferroelectricity. (2) The sum of higher order (than three-body) interactions are shown to be more important than three-body interactions (which are small); when v approaches 0.208, the higher order terms are comparable to the two-body term. (3) Finite 1D chains of N atoms behave like infinite chains when N exceeds 100. (4) 1D surface tensions deviate from two-body predictions for large values of the coupling parameter (v > 0.10).

AB - Van der Waals dispersion forces are examined for an infinite one-dimensional (1D) chain of atoms. Building on the work of Bade and Kirkwood (J. Chem. Phys. 27, 1284, 1957), dipolar fluctuations of the 1D chain are analyzed in terms of polarization waves. The van der Waals energy of the chain is evaluated from the zero-point energy of these waves. Several results are found. (1) A critical value exists for the dimensionless coupling parameter v = α0/a3, for large polarizabilities (α0) or small lattice spacings (a). When v > 0.208, the 1D line has divergences in both the dispersion relation of the waves and the effective site polarizability. The resulting instability is analogous to 1D ferroelectricity. (2) The sum of higher order (than three-body) interactions are shown to be more important than three-body interactions (which are small); when v approaches 0.208, the higher order terms are comparable to the two-body term. (3) Finite 1D chains of N atoms behave like infinite chains when N exceeds 100. (4) 1D surface tensions deviate from two-body predictions for large values of the coupling parameter (v > 0.10).

UR - http://www.scopus.com/inward/record.url?scp=52149095668&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52149095668&partnerID=8YFLogxK

U2 - 10.1080/00268970802195066

DO - 10.1080/00268970802195066

M3 - Article

AN - SCOPUS:52149095668

VL - 106

SP - 1587

EP - 1596

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 12-13

ER -