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Unformatted text preview: 1 Lecture-Notes for “NanoMechanics” (figures, detailed derivations and examples not included) Dr. CQ Ru (Dept. of Mech. Eng, Univ. of Alberta, Canada) Contents 1 Surface Forces at Nano/Micro Scale van der Waals forces Casimir forces Electrostatic forces Capillary forces 2 Adhesion Mechanics JKR model of contact mechanics Tip-surface interaction and adhesion Adhesion by capillary forces Surface instability of compliant solids 3. Micro/Nano Beams and Nanotubes Casimir forces in MEMS/NEMS Simple spring model for microbeam arrays Dissipation in MEMS/NEMS Surface stress effect on nanowires (NWs) Elastic models for carbon nanotubes 4. Mechanics of Graphene Elastic properties of graphene sheets Vibration of graphene sheets Wrinkling and fracture of graphene sheets 5. Microflows Fluid flow with boundary slip Fluid flow at low Reynolds number Electrokinetic flow Capillary flow 6. Cell Mechanics 7. Molecular Dynamics (MD) simulations 1. Surface Forces at Nano/Micro Scale Nanomaterials are defined as the materials which have at least one dimension (such as thickness, width, or diameter) between a few nanometers to a few hundreds of nanometers. Examples : 0D : C60, quantum dots, nanoparticles. 1D : nanowires, nanobelts, nanotubes, DNA molecules. 2D: nano-films, graphite sheet, monolayer. Nanomechanics : One major new feature of nanomechanics is the significance of some “weak” surface forces which are negligible (say, 2 as compared to body forces) in macro-mechanics but become dominant (over traditional forces) at the nanoscale. Example : Surface forces become dominant over body forces (Pelesko & Bernstein, “Modeling MEMS and NEMS”, p74-75, bending deflection of a cantilever elastic beam). 1-1. Van der Waals Forces The term “van der Waals” follows after the van der Waals eqn. (1879) –the first successful phenomenological model which accounts for the role of intermolecular forces in real gas (a refined model for the earlier Boyle “ideal” gas model) RT b V V a p ) )( ( 2 , a modified form of perfect gas eqn. RT pV where R=the universal gas constant, p=pressure, V=volume, T=temperature, and a and b are two positive constants – a represents the role of long-distance (van der Waals) attractive intermolecular forces which reduces the outward pressure on the walls of the container, and b represents short-distance repulsive forces which causes a finite hard core volume deducted from the total volume V. 1-1-1. The Origin of van der Waals Forces Atoms are electrically neutral as a whole. Atoms of a molecule are bonded together by electrostatic ( covalent ) forces through sharing common electrons in their outer shells, in order to fill the vacancies of the outer shells and lower the total energy (like car poll which lowers the cost). Even though individual molecules are neutral in electrical change, they have unbalanced (permanent, induced, or instantaneous) electric dipole moment caused by the non-coincidence of the center of positive changes and the center of negative changes carried by moving...
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This note was uploaded on 09/27/2011 for the course ECON econ 546 taught by Professor Dmdj during the Fall '11 term at ECCD.
- Fall '11