Are mechanical laws different at small scales YES

Are mechanical laws different at small scales? YES! If we scale quantities by a factor ‘S’ Area a S 2 Volume a S 3 Surface tension a S Electrostatic forces a S 2 Magnetic forces a S 3 Gravitational forces a S 4 • Surface Area/Volume effects • Stiction: “Sticky friction”, due to molecular forces - surface tension pulls things together SCALING OF: Mechanical systems Fluidic systems Thermal systems Electrical and Magnetic systems Chemical and Biological systems

Which dynamical variables are scaled? - depends on our choice e. g. Mechanical systems Constant stress Scale independent elastic deformation, scale independent shape Electromagnetic systems Constant electrostatic stresses/field strengths Thermal systems Constant heat capacity & thermal conductivity

Scaling Issues in Fluids Viscosity & Surface Tension • Definition: A fluid cannot resist shear stresses Re is the ratio of inertial and viscous forces, v: velocity, r: density. l: linear dimension Viscosity dominates at: Re < 1 Re for whale swimming at 10 m/second ~ 300, 000 Re for a mosquito larva , moving at 1 mm/sec ~ 0. 3 Re marks the transition between Laminar/Smooth flow & Turbulent Flow (mixing) In MEMS: always laminar flow!

Thermal Issues Easier to remove heat from a smaller sample • Thermal Mass (specific heat X Volume) scales as l 3, but heat removal scales as l 2 (proportional to area) • Evaporation or Heat loss increases as Surface Area/Volume increases

Electrophoresis - Stirring vs. Diffusion, Diffusion is the dominant mixing process in MEMS - Separation of bio-molecules, cells by the application of electric fields E=0 E>0 Separation of different types of blood cells

Miniature Clinical Diagnostic Systems Fast, on-site, real time testing Principle: High Isolation, Low Mass, Localized heating possible • Polymerase Chain Reaction (PCR) for DNA amplification Micro-fabricated DNA capture chip (Cepheid, CA) Scaling of Minimal Analytic Sample Size

Scaling in Electricity and Magnetism • Potentiometric devices (measure voltage) are scale invariant • Amperometric devices (measure current) are more sensitive when miniaturized e. g. , m-array electrochemical detectors (Kel-F) for trace amounts of ions Electroplating is faster in MEMS Courtesy: M. Schoning

Scaling in electromagnetic systems Constant electrostatic stresses/field strengths Voltage Electrostatic field · length L Resistance Length L-1 Area Ohmic current Voltage L 2 Resistance Current density (I/A) is scale invariant

Scaling in Electricity and Magnetism Electric: e: dielectric permittivity (8. 85. 10 -12 F/m) E: electric field (Breakdown for air: 30 k. V/cm) Magnetic: m: permeability (4 p. 10 -7 N/A 2) B: Magnetic field Rotor Stator Sandia MEMS Human Hair !

Electrostatics is more commonly used in MEMS Macroscopic machines: Magnetic based Microscopic machines: Electrostatics based Judy, Smart Mater. Struc, 10, 1115, (2001)

Electrostatics vs. magnetostatics Electrostatic force Area · (Electrostatic field)2 L 2 Electrostatic energy Volume · (Electrostatic field)2 L 3 Magnetic field Current L distance Magnetic force Area · (magnetic field)2 L 4 Magnetic forces are much weaker compared to electrostatic forces Magnetic energy Volume · (Magnetic field)2 L 5

Power and Power density scaling Power Force · speed L 2 Power density Power L-1 Volume Small devices made through strong materials can have very large power densities e. g. 10 n. N force in a 1 mm 3 volume ~ 103 J/mm 2 c. f. a thin-film battery ~ 1 J/mm 2

Power in MEMS Compact power sources needed, but Power scales by mass Currently: Fuel cells, micro-combustors, Radio frequency/optical sources Energy stored in 1 mm 3 Power capacitor 4 m. J/mm 3 1 m. W for 4 s Thick Film Battery 1 J/mm 3 Thin Film Battery 2. 5 J/mm 3 270 m. W for 1 hour 0. 7 m. W for 1 hour Solar Cell (1 X 0. 1 mm 3) 0. 1 m. W Gasoline 300 J/mm 3 3 m. W for 1 day 178 Hf > 10 MJ/mm 3 160 m. W

MEMS devices: How do we make them? A mechanism Gear chain Sandia MEMS Hinge Gear within a gear

Making MEMS • How to make a MEMS device - deposit and etch out materials • Introduction to Micro-machining - Wet and Dry etching - Bulk and surface micro-machining • What kinds of materials are used in MEMS? -Semiconductors - Metals - Polymers