Lecture Density

Lecture 3: Density System property = mass
Material property = density (ρ = m/V) Solid state density depends on atomic mass and packing efficiency. Range: 700 kg/m3 (hydrocarbon polymers) – 20000 kg/m3 (Au, Pt, W…) Lower densities achieved by incorporating porosity e.g. Aerogels (20-100 kg/m3)

Useful reference values Gold Iron Concrete Water Polyethylene Wood Aerogel Air

19300 kg/m3 7900 kg/m3 2600 kg/m3 1000 kg/m3 925-960 kg/m3 460-670 kg/m3 20-100 kg/m3 1.2 kg/m3 All values quoted for room temperature

When is density important? • When components have to be moved or supported
transport, structures • Maximise kinetic energy / volume
flywheel, bullets Also related to many other materials properties e.g. speed of sound: v = (E/ρ)1/2 v = speed of sound in the material E = material stiffness ρ = density

(Newton-Laplace equation)

Tailoring density by introducing porosity • Natural materials e.g. limestone, sandstone (incomplete consolidation of particles), wood and bone (cellular structure)

• Foams – polymer, metal, ceramic • Calcium silicate brick • Aerogels

Foams

© NPL

Applications:

structural materials blast protection thermal insulation

Fabrication methods:

foaming agent direct injection of gas into molten material pour melt into preform, which then decomposes or dissolves

Calcium silicate board 90% porosity

30 m Scanning electron microscope view, A. Hamilton, 2002

Aerogels “Frozen smoke” – 99% porosity

Applications: thermal insulation e.g. double glazing

Aerogels Fabrication method: Sol-gel processing

Extraction of solvent

Silica nanoparticles

Wet gel

Aerogel

Calculating density and porosity ρb = ρs(1-f ) ρb = bulk density ρs = solid density f = pore volume / total volume

(see tutorial sheet 2)


simple example of law of mixtures for composite material: Xb = ΣfiXi Xb = property of bulk composite material Xi = property of individual component fi = volume fraction of individual component

Influence of porosity on material properties • Density • Thermal conductivity • Thermal expansivity • Stiffness • Strength • Liquid transport (particularly in construction materials)
distinguish between open and closed porosity