Laser Diffraction Us er Day
The Link Between Different Particle Characterization Techniques: Laser Diffraction, Imaging and Rheology
Dr Adrian Hill Product Technical Specialist – Rheometry (45 mins) Malvern Instruments Limited, UK Etten-Leur September 2015 Over view › Basic Concepts . Rheology and “associated structure” . Volume Fraction › Effect of size and volume fraction › Effect of particle share B ASIC CON CEPTS What is “ Rheology” …
› Rheology; from the Greek word rheos & logos . Rheos - stream current (i.e. flowing) . Logos – the study of…
› The technical definition is: . “The science of deformation and flow”
› In practice it is used as a problem solving tool… . My material…. • will not pour • is not stable • will not spray • is settling • leaves trail marks Rheology Testing › When it typical rheological testing, we tend to split the testing up into flow (viscosity) and deformation (oscillation) type testing “the science of deformation and flow” FLOW DEFORMATION Measure the VISCOSITY of a sample Quantifies VISCOELASTICITY Mimics typical processing conditions How does a sample behave before a sample flows…? The resistance to flow Predicts sample properties
How thick is a paint sample Stiffness of the material Will the sample be pumped? Sample classification (solid, liquid) Sample stability – will it settle? What is Rheology at the Particle Level › Rheology can be considered the measurement of structure . More associated structure gives more rheology (over Newtonian behaviour) . Viscosity is resistance to flow, more associated structure, more resistance › This association structure is typically from particle (and molecule) interactions (at higher concentrations) . Colloidal interactions, electrostatic, hydrogen boning, steric… etc › Change the particle properties, changes the rheology . Size (length), polydispersioty (MWD), shape, charge (zeta), volume fraction . Rheology is a bulk material property, related to what goes into the material Flow Curve Measurements – Particle Association “ YIELD STRESS” An ever increasing viscosity as the shear rate approaches zero, i.e. a does not flow / solid like when stationary.
ZERO SHEAR VISCOSITY The viscosity plateau’s as the shear rate approaches zero, i.e. flows / liquid like Viscosity when stationary. Log
Rheometer measurement range Viscometer Measurement range
-6 6 10 Log Shear Rate 10 Studying weaker Studying stronger interactions interactions Reason for Shear Rate Dependency › Entanglement Network / Particle-Particle-Interaction η Log
. Log γ
Equilibrium Destruction > No Entanglements Recovery Molecules / Particles Entanglements / Particle Interaction More “ Rheology” from increase in viscosity
› A rheometer is a very powerful tool to probe the internal structure of a material › In this presentation we will generally consider the affect on “viscosity”, however more viscosity leads to more “rheology” › When viscosity increases, the following are typical . Any yield stress, increases . Any thixotropic can increase . Oscillation, linear region changes • Decreases as more “brittle” . Oscillation, more solid like nature • Viscoelastic liquid to viscoelastic solid changes • Phase angle decreases Mastersizer 3000 Kinexus Rheometer
PARTICLE SIZE INFLUENCE Effect of particle size - non-colloidal systems › For non-Colloidal particles the effect of particle size on viscosity should be minimal as shown below › The most critical factor governing viscosity is the volume fraction of particles in suspension
Effect of particle size on relative viscosity at various volume fractions of spherical particles (Lewis and Nielsen). Colloidal Suspension Rheology Jan Mewis, Norman J. Wagner, 2012 Effect of particle size - colloidal systems › For small particles colloidal effects can be significant . Brownian motion . Attractive/Repulsive forces › Inter-particle forces dominate at low shear rates giving a large increase in shear stress and hence viscosity › Hydrodynamic (fluid) stresses dominate at high shear rates, hence particle size effects are minimised Effective volume fraction › Solid volume fraction may be constant with particle size but volume in solution may not L › Adsorbed or charged layers will increase hydrodynamic size and
effective volume (ᶲeff) in solution › This effective volume fraction will increase with decreasing size a 3 L φeff =φ1+ 2a › Where L is particle separation and a is the radius Effect of particle size on effective volume
L = 0.5um, a = 1um, ᶲ = 0.2 › This gives an effective volume L fraction of 0.39 › This equates to almost 100% increase in volume
L = 0.5um, a = 5um, ᶲ = 0.2 a › This gives an effective volume fraction of approximately 0.23 › This equates to a 15% increase in volume Effect of particle loading
› Krieger-Dougherty equation −[η ]φ η φ m =1− η medium φm
η – viscosity of the suspension
ηmedium – viscosity of the medium φ – volume fraction of solids in the suspension
φm – maximum vol. fraction of solids in the suspension [η] – intrinsic viscosity of the medium (2.5 for spheres) Volume fraction, φ
› Describes the amount of particles in a material. › φ – volume fraction of solids in a suspension
› φm – maximum volume fraction of solids in the suspension (i.e. the maximum free room the particles have to move around in). Increase φ
φ <<< φm φ < φm φ ∼ φm Effect of particle loading
› As volume fraction (φ) increases…
−[η ]φ η φ m =1−
Log cos Vis ity η medium φm
Volume fraction of particle › The n vis cos ity (η) increases. › Packing more molecules makes flow more difficult. Controlling flow behaviour
› Changing the volume fraction… Newtonian Shear Thinning Shear Thickening φ φ φ <0.1 0.1< <0.5 >0.5 φm φm φm Log cos Vis ity
Volume fraction of particle Shear thickening of concentrated dispersions
› Shear thickening effects can have negative impact on process-ability Why? Colloidal microstructure and viscosity
Colloidal Suspension Rheology Jan Mewis, Norman J. Wagner, 2012 Effect of particle size distributions
› We can keep the volume fraction (φ) the same. › Now, change the particle size distribution… Particle Size Distribution 20
15
10
Volume (%) 5
0 0.1 1 10 100 1000 3000 Particle Size (µm)
› What happens to the viscosity? Effect of Distribution on Maximum Packing Fraction
› As the particle size distribution increases, this allows a greater packing fraction.
Random Random polydisperse monodispersed close packing close packing
φm ≈ 0.62 φm ≥ 0.74 Effect of Maximum Packing Fraction
› As maximum packing fraction increases…
−[η ]φ η φ m = − Constant 1 volu m e Vi s c o s i t y η medium φm fraction
Volume fraction of particle › The n vis cos ity (η) decreases. › Allows more free flowing particles (self lubricating) Pr actical Example
› Different sized talc added to an epoxy
All 175 μm
Vi s c o s i t y All 750 μm
0% Increasing amount of 175 μm 100%
100% Increasing amount of 750 μm 0% Morphologi G3 Kinexus Rheometer
PARTICLE SHAPE INFLUENCE Over view › A main assumption here was that our particles are ideally smooth, non-deformable spheres… › …however, real solid particles tend not to be perfectly smooth spheres but come in various shapes and with various surface irregularities . Fibers, Plates, Grains, Tubes…… Particle orientation in suspension › Both shear and Brownian forces will cause particles to rotate or tumble in the liquid › The viscosity is dependent on the resulting orientation . Viscosity lowest when long axis is parallel to flow direction . Viscosity highest when long axis is perpendicular to flow direction › Elongated particles circumscribe a larger circular paths than a sphere of equivalent volume… › …thus they occupy larger volumes in suspension at lower shear rates Effect of aspect ratio on Viscosity
› Zero shear relative viscosities ( r) increase with aspect ratio as shown below for a Tobacco Mosaic Virus › Consequently elongated particlesƞ are much more efficient at increas ing vis cos ity than s pherical particles of the same volume
a
b Colloidal Suspension Rheology Jan Mewis, Norman J. Wagner (2012), citing Laufer (1944) Surface roughness › Surface roughness can cause deviations from smooth particle behaviour › Surface roughness may increase viscosity due to an increasing surface area and divergence in flow lines . Most prominent with small particles › For very rough particles mechanical friction from particle-particle contact can increase viscosity… › …although divergence in flow field around the particle can also hinder close contact – lowering viscosity . Most prominent in conc. systems Viscosity and particle shape – conc. systems › Krieger-Dougherty equation −[η ]φ η φ m =1− η medium φm
› φm – max vol. fraction of solids in suspension › [ ] – intrins ic vis cos ity of the m edium › Comη plex particle and fluid interactions give a non-linear viscosity dependence with particle concentration › This behavior has shown to be well characterized using an equation of this form Effect of particle shape in concentrated systems
› As aspect ratio increases ϕm decreases and [ ] increases . Exponent ([ƞ] ϕ ) tends to stay approximate the same ≈ 2 m ƞ
−[η ]φ η φ m =1− η medium φm Vi s c o s i t y
› Th e n vis cos ity (η) increases Volume fraction of particle › Deformable particles can change shape to accommodate more material hence ϕm increases and [ ] decreases ƞ Flow Behaviour of hard particles › Under shear, elongated particles can align in flow direction due to hydrodynamic forces acting on the particles
102 › Under 101 shear ) 100 Pa.s (
η 10-1
10-2 › At rest
10-2 10-3 10-1 100 101 102 103 γ (s -1) › Therefore, elongated particles tend to shear thin more than spherical particles. Flow behaviour of deformable / soft particles › Shear can deform soft spheres to form elongated particles at higher shear rates
102 › Under 101 shear )
0 Pa.s
( 10 η 10-1 › At rest
10-2
10-2 10-3 10-1 100 101 102 103 γ (s -1) › Therefore, deformable particles (e.g. emulsions) tend to shear thin more than hard particles dispersions Summary › Rheology, a bulk property, is affected by what goes into a material › Rheology is a measurement of the internal “associated” structure › Particle properties going into a system affects the particle interactions . Affect these interactions, affect the rheology . Size (length), polydispersioty (MWD), shape, charge (zeta), volume fraction › In general: . Reduce the particle size in colloidal particulate systems increase the rheology (viscosity) . Increase the polydispersity in particulate systems, increase the rheology . Change the shape (increase elongate, surface roughness) also increases rheology The End
Any questions?
adr ian.hill@malver n.com www.malvern.com
References
› Barnes, H A (1992), Recent advances in rheology and processing of colloidal systems, The 1992 IChemE Research Event, pp. 24-29, IChemE, Rugby › Derjaguin, B; Landau, L (1941) Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes, Acta Physico Chemica URSS 14, 633. › Hunter, R.J (1988), Zeta Potential in Colloid Science: Principles and Applications, Academic Press, UK. › Larson, R.G (1999), The Structure and Rheology of Complex Fluids, Oxford University Press, New York › Verwey, E. J. W.; Overbeek, J. Th. G. (1948), Theory of the stability of lyophobic colloids, Amsterdam: Elsevier › P. B. Laxton and J. C. Berg. Gel trapping of dense colloids. J. Colloid Interface Sci. 285:152–157 (2005