The Stochastic Dynamics of an Array of Micron Scale Cantilevers in Viscous Fluid

The stochastic dynamics of an array of closely spaced micron scale cantilevers in a viscous fluid is considered. The stochastic cantilever dynamics are due to the constant buffeting of fluid particles by Brownian motion and the dynamics of adjacent cantilevers are correlated due to long range effects of fluid dynamics. The measurement sensitivity of an experimental setup is limited by the magnitude of inherent stochastic motion. However, the magnitude of this noise can be decreased using correlated measurements allowing for improved force resolution. A correlated scheme is proposed using two atomic force microscope cantilevers for the purpose of analyzing the dynamics of single molecules in real time, a regime that is difficult to observe using current technologies. Using a recently proposed thermodynamic approach the hydrodynamic coupling of an array of cantilevers is quantified for precise experimental conditions through deterministic numerical simulations. Results are presented for an array of two readily available micron-scale cantilevers yielding the possible force sensitivity and time resolution of correlated measurements. This measurement scheme is capable of achieving a force resolution that is more than three fold more sensitive than that of a single cantilever when the two cantilevers are separated by 200 nm, with a time scale on the order of tens of microseconds.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mechanical Engineering

Department dc:contributor.department

Mechanical Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2006

Author dc:creator

• Clark, Matthew Taylor

Chair dc:contributor.committeechair

• Paul, Mark R.

Committee members dc:contributor.committeemember

• Tafti, Danesh K.
• Vick, Brian L.

• correlated
• fluid coupling
• stochastic
• atomic force microscope

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-07312006-122845

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/34275