Special Section on Nanostructures Honoring Craig F. Bohren

Many-body van der Waals forces involving chains

[+] Author Affiliations
Milton W. Cole

The Pennsylvania State University, Physics Department, University Park, PA 16802

Leonidas N. Gergidis

The Pennsylvania State University, Department of Chemical Engineering, 108 Fenske Lab, University Park, PA 16802

Jessica P. McNutt

The Pennsylvania State University, Department of Curriculum and Instruction, University Park, PA 16802

Darrell Velegol

The Pennsylvania State University, Department of Chemical Engineering, 108 Fenske Lab, University Park, PA 16802

Hye-Young Kim, Zachary K. Bond

Southeastern Louisiana University, Department of Chemistry and Physics, Hammond, LA 70402

J. Nanophoton. 4(1), 041560 (April 16, 2010). doi:10.1117/1.3427144
History: Received December 5, 2009; Revised April 6, 2010; Accepted April 12, 2010; April 16, 2010; Online April 16, 2010
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Abstract

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.

© 2010 Society of Photo-Optical Instrumentation Engineers

Citation

Milton W. Cole ; Leonidas N. Gergidis ; Jessica P. McNutt ; Darrell Velegol ; Hye-Young Kim, et al.
"Many-body van der Waals forces involving chains", J. Nanophoton. 4(1), 041560 (April 16, 2010). ; http://dx.doi.org/10.1117/1.3427144


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