Chapter 1. Particle Size Analysis - CHERIC

1 Chapter 1. Particle size IntroductionParticle size / Particle size distribution: a key role in determining the bulk properties of the size ranges of particles (x)- Coarse particles : >10 m- Fine particles : 1 m- Ultrafine(nano) particles : < m (100nm) Describing the size of a Single ParticleDescription of regular-shaped particles : Table diameters- Martin's diameter- Feret diameter- Shear diameterEquivalent (sphere) diametersFigure Equivalent volume (sphere) diameters:the diameter of the hypothetical sphere having the same volumexv=(6V )1/3- Equivalent surface diameter:the diameter of the hypothetical sphere having the same surface areaxs=(S )1/2- Surface-volume diameter: the diameter of the hypothetical sphere having the same surface-to- volume ratio xsv=6VS"Which diameter we use depends on the end use of the information.

2 "Worked Example Example Description of Population of ParticlesParticle size diameter, x( m)Figure distribution fN(x), [fraction] fN(x)dx: fraction of Particle counts (numbers) with diameters betweenx and x+dx Cumulative distribution : , [fraction]fN(x)=dFN(x)dx Mass(or volume) distribution fM(x),(mass fraction/ m)fM(x)dx:fraction of Particle mass with diameters betweenx andx+dxfM(x)dx= p 6x3fN(x)dx 0 p 6x3fN(x)dx=x3fN(x)dx 0x3fN(x)dx=fV(x)Surface-area size distribution functionfS(x)dx= x2f(x)dx 0 x2f(x)dx=x2f(x)dx 0x2f(x)dxFigure Conversion Between DistributionsFrom abovefM(x)=fV(x)=x3fN(x) 0x3fN(x)dx=kVx3fNwhere kV=1 0x3fN(x)dxfS(x)=x2fN(x) 0x2fN(x)dx=kSx2fNwhere kS=1 0x2fN(x)dxfM(x)=fV(x)=kVx3fN=kVx3fS(x)kS x2=kVkSxfS(x)where kV=1 0x3fN(x)dxWorked Example Example Example Describing the Population by a Single Number 1) AveragesMode: most-frequent sizeMedian: x at F(x)= Mean: Table general, g(x)= 0g(x)f(x)dx= 10g(x)dF(x) - Arithmetic mean.

3 G(x)=xx= 0xf(x)dx= 10xdF(x)where F(x) can be FN(x), FS(x) and FV(x)* Also called first moment averageIf F(x)=FN(x), xaN= 10xdFN Arithmetic mean diameter of number distributionIf F(x)=FS(x), xaS= 10xdFS= 10xdFS 10dFS= 10x3dFN 10x2dFN=xSV Arithmetic mean diameter of surface area distribution Surface-volume mean diameter (Sauter mean diameter)- Geometric mean (g(x)=lnx)logxg=logx=[ 10logxdF]- Harmonic mean (g(x)=1x)1xh=[ 101xdF]Figure example ) Standard deviation =[ 0(x-x)2dF(x)]1/2=[ 0(x-x)2f(x)dx]1/2 Degree of Common Methods of Displaying size Distribution 1) Arithmetic Normal(Gaussian) distribution:Figure (x)dx=1 2 exp[-(x-x)22 2]dxand =x84%-x50%=x50%-x16%= (x84%-x16%)- Hardly applicable to Particle size distributionFigure particles : no negative diameter/distribution with long tail2) Lognormal distribution : x lnx ln g.

4 F(lnx)dlnx=1(ln g)2 exp[-(lnx-lnx)22(ln g)2]dlnxwhere lnx= 10lnxdF(x)= 10lnxdF(lnx)= - lnxf(lnx)dlnx=lnxg xg: geometric mean(median) diameter ln g=[ 0(x-x)2dF(x)]1/2=[ - (lnx-lnxg)2f(lnx)dlnx]1/2 g : geometric standard deviationFigure g=x84%x50%=x50%x16%=[x84%x16%]12 Fullerene-named after the architect, Buckminster Fuller, who designed "Geodesic dome" * Dispersity criterion - Monodisperse : =0 or g=1, in actual g < - Polydisperse: g> (or ) Understanding size of NanoparticlesComparison with bulk110102103104105106 MoleculesNanoparticlesBulkNumber of moleculesParticle diameters, 107107100 Full-shell clustersAtoms(molecules) in nanoparticlesExtremely small nanoparticles!

5 * Polymers-Nanoparticles? , in where (molecular weight) and (density) in cgs unitsExample. 100,000 1g/cm3 , .* Biological substance-Nanoparticles? , in * Special nanoparticles(nanomaterials)-carbon size -Related Properties of Nanoparticles* Finite size effect - small number of atoms and electrons* Surface/interface effect - large fraction of active surface a sphere with a diameter with a diameter of 1um. If this mass of sphere is converted (through a size reduction process) to spheres with a diameter of 1nm, calculate the increase in surface area of the smaller sized Levels in Semiconductor and Metal particles (1) Quantum size (confinement) effects- Small number of atoms and electron as size decreases(<de Broglie wavelength*)Optical properties of semiconductors- Rapidly increase in band gap with a decreasing size - Blue shiftCoulomb blockade(2) Surface plasmon resonance of metal nanoparticles- Coherent excitation of all the free electrons by light, leading to an in-phase oscillation for particles ( lightxl< )- Intense SP absorption bands at a certain wavelength(3)

6 Coulomb BlockadeOhm's law, , I is linear with respect to VA single electron can be added when or where For bulk materials ( ), and For nanoparticles ( ), and When and * Single electron transistor(3) Magnetic properties of ferromagnetic particles - Ferromagnetic materialsAtoms: unpaired electrons domain formationBulk: multidomaincf. diamagnetism, paramagnetism- Behavior of ferromagnetic materials under magnetic field: BH diagram- For small particles (nmx100~10:), single domain is in the lowest energy state "Single- domain particles " . Used for magnetic recording media- For smaller particles (nmx15<) . Thermal fluctuation > magnetic alignment as the size decreases "Superparamagnetism".

7 No hysteresis loop and high Ms . Used in biomedical application, ferrofluids, Methods of Particle size Measurement1) Sieving2) MicroscopyElectron microscopy3) Sedimentation4) Permeametry5) Electrical methods. Electrical mobility. Electrozone sensing6) Laser Diffraction. Optical Particle counter. Photon correlation spectroscopy (dynamic light scattering)