TY - JOUR

T1 - Many-body van der Waals forces involving chains

AU - Cole, Milton W.

AU - Gergidis, Leonidas N.

AU - McNutt, Jessica P.

AU - Velegol, Darrell

AU - Kim, Hye Young

AU - Bond, Zachary K.

N1 - Funding Information:
We thank Craig Bohren for his many valuable insights into our work in using the coupled dipole method for calculations of van der Waals forces. We gratefully acknowledge support from DOE grant (DOE-FG02-07ER46414) and discussions with Austin Ostrowski, who helped in early stages of this project. H.-Y. Kim thanks David Norwood for helpful discussions.

PY - 2010

Y1 - 2010

N2 - Van der Waals (VDW) forces arise from quantum mechanical fluctuations of local charge densities. Whereas computing VDW interactions between two atoms requires only 2-body interactions, by definition, computing interactions between macroscopic bodies required multi-body interactions, where the presence of a third atom affects how any two atoms interact, and a fourth atom affects the first three, and so on. Often, 3-body interactions have been found to be small, and 4-body and higher interactions are almost always neglected in calculating interactions between atoms. But is it possible that 4-body and higher order interactions can actually be more important than 3-body interactions, and indeed comparable to 2-body interactions? We explored the following question: how important is the sum of 4-body and higher order interactions? A set of problems involving finite and infinite chains was explored numerically and analytically, including a single chain, a pair of parallel, long chains and a two-dimensional array of long, parallel chains. The "coupled dipole method" was used, providing a type of "nanoscale Lifshitz theory" for calculations of nanoscale VDW interactions. Calculations were made for the static polarizability, as well as the VDW interaction between chains. This latter energy was compared with that found by summing 2-body interactions for the chains. It was found that when a "coupling constant" ν, which is the polarizability per unit volume of the material, is large, then the sum of 4-body and higher order interactions dominates both the 2-body and the 3-body interactions. In addition, it was found that for all geometries examined, a divergence of the polarizability and a dynamical energy instability occur simultaneously when ν reaches a limiting value νmax, giving a well-known polarization catastrophe.

AB - Van der Waals (VDW) forces arise from quantum mechanical fluctuations of local charge densities. Whereas computing VDW interactions between two atoms requires only 2-body interactions, by definition, computing interactions between macroscopic bodies required multi-body interactions, where the presence of a third atom affects how any two atoms interact, and a fourth atom affects the first three, and so on. Often, 3-body interactions have been found to be small, and 4-body and higher interactions are almost always neglected in calculating interactions between atoms. But is it possible that 4-body and higher order interactions can actually be more important than 3-body interactions, and indeed comparable to 2-body interactions? We explored the following question: how important is the sum of 4-body and higher order interactions? A set of problems involving finite and infinite chains was explored numerically and analytically, including a single chain, a pair of parallel, long chains and a two-dimensional array of long, parallel chains. The "coupled dipole method" was used, providing a type of "nanoscale Lifshitz theory" for calculations of nanoscale VDW interactions. Calculations were made for the static polarizability, as well as the VDW interaction between chains. This latter energy was compared with that found by summing 2-body interactions for the chains. It was found that when a "coupling constant" ν, which is the polarizability per unit volume of the material, is large, then the sum of 4-body and higher order interactions dominates both the 2-body and the 3-body interactions. In addition, it was found that for all geometries examined, a divergence of the polarizability and a dynamical energy instability occur simultaneously when ν reaches a limiting value νmax, giving a well-known polarization catastrophe.

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U2 - 10.1117/1.3427144

DO - 10.1117/1.3427144

M3 - Article

AN - SCOPUS:80455149786

VL - 4

JO - Journal of Nanophotonics

JF - Journal of Nanophotonics

SN - 1934-2608

IS - 1

M1 - 041560

ER -