CH5716 Processing of Materials Ceramic Thick Film Processing Lecture MC5 Slurry Characterisation
Specific Surface Area Powder size & specific surface area (area per unit wt) closely related As particle size decreases so SSA increases At very small sizes surface area becomes dominant due to ratio of surface to volume Very fine particles may lead to enhanced sintering However high surface area also has implications in green stage processing. Effects on Green stage Processing of High Surface Area Powders Tendency to floc; large surface area to volume (mass) ratio, electrostatics, Van der Waals etc become more dominant. Difficult to disperse more dispersant required to coat higher surfaces Interaction with solvents and binders can increase slurry viscosities resulting in lower solids loadings Therefore Specific Surface Area is an important parameter to know Some would argue the most important Most often measured by nitrogen absorption using BET method 5-15m 2 /g common for tape castingup to 36m 2 /g has been used for screen printing
Particle Size and Size Distribution Particle Size often quoted as a D 50 Not really helpful as powders with same D 50 can have very different distributions Better to quote D 10 & D 90 values as well Gives some idea as to distribution Often quoted more than SSA, however SSA more influential- especially in irregular particles Narrow distribution will lead to good even densification Wide distribution may result in a tendency to coarsen larger particles seed grain growth Laser Scattering has become dominant technique replacing sedimentation Accuracy Speed Small sample size Automation possible Care must be taken in sampling, especially in large batches Interpretation of results also requires care Augmenting early results with SEM data useful
Laser Scattering Particle Size Analysis Basic light scattering Relationship between scattering angle θ and d is Sinθ = 1.22λ/d (small particles scatter more) Limited by λ (eg He-Ne laser λ = 0.63µm) Only truly accurate at 2-100+µm Inaccuracies creep in at sub micron levels Over-estimation of fine fraction Mie Theory involves complex solution of Maxwell Eqns More accurate for sub micron particles Used in most of the commercial software Requires both Real & Imag. Refractive Indices Some approximation required for new materials
Assessing Dispersion Generally we assume our 24 hours has done the trick established formulation However new powder or formulation may change things 2 possible methods to check - sedimentation and sizing Sedimentation also useful for optimising dispersant level Discussed later Sedimentation Method Best applied as an initial technique on new slurry to ensure all is OK Not really in line QA test Agglomerates present - low packing density Take 10ml sample from mill at set intervals over a predetermined time These samples should be but into 10ml graduated cylinders and allowed to settle May take several days Once settled note height of sediment and clarity of supernatant A t full dispersion sediment height will reach a minimum. Well dispersed high sediment density
Assessing Dispersion with PSA Volume (%) Volume (%) Utilise internal ultrasound capabilities in PSA -Malvern Mastersizer 2000 This is designed to deagglomerate powders when characterising raw materials before processing. Initial sizing is measured straight from bottle after milling. (only a few drops required) Ultrasound is then applied to specimen for around 5 minutes. 8 7 6 5 4 3 2 1 Particle Size Distribution 0 0.01 0.1 1 10 100 1000 3000 Particle Size (µm) AQ YSZ tape 1-test 2, 06 October 2010 12:00:34 Run 1; as milled d 10 = 0.12, d 50 =0.318, d 90 =1.101 Second sizing measured from sample- If this result is comparable to initial measurement then deagglomeration appears complete. If a size reduction is observed further milling required. Fast technique, can be used as in-line QA. Care must be taken to avoid sampling errors. Alternate method would be to take 2 measurements across a set time interval 8 Particle Size Distribution 7 6 5 4 3 2 1 0 0.01 0.1 1 10 100 1000 3000 Particle Size (µm) AQ YSZ tape 1-test 2, 06 October 2010 12:08:14 Run 2; after 5 min US d 10 = 0.12, d 50 =0.315, d 90 =1.073
Optimising Dispersant Level Sediment Height Similar methodology to previously discussed experiment This time powder is milled for 24 hrs with each dispersant level Settling as before over a few days Once fully coated minimum height is reached Too much dispersant can often be seen by discolouration of supernatant fluid Other approaches PSA Taking sizing reading at each dispersant level As dispersion improves agglomerate peak should reduce while primary peak increases 0 0.5 1 1.5 2 2.5 Wt % Dispersant Observation Viscosity As dispersion increases minimum viscosity should be observed. Measurement of batches with varying dispersant levels Repeated assessment of viscosity as dispersant level is increased Can have issues in non Newtonian systems
Viscosity Shear Stress Rheology of Slurries and Pastes Newtonian Flow A x V Consider a fluid with parallel planes with area A A force is applied to the top plane while the bottom plane remains stationary The force results in the top plane moving with velocity V This creates a velocity gradient across the thickness of the fluid, x Velocity gradient = dv/dx = shear rate, γ, s -1 (ms -1 /m) Shear stress, τ = F/A (Newton/m 2 = Pascal (Pa)) For a Newtonian fluid τ is proportional to γ τ = η γ where η is a constant, the co-efficient of viscosity in Pa.s So η= τ / γ and will be a straight line through the origin when plotted on a graph of shear stress against shear rate. Although Pa.s is the SI unit poise or centipoise often used in industry 1Pa.s = 10poise 1mPa.s= 1 centipoise Shear rate Shear rate
Non-Newtonian Flows Unfortunately slurries, slips and pastes do not behave in a Newtonian fashion Polymer chains, particles, agglomerates and their interactions all get in the way Families of non-newtonian Flow Pseudoplastic Dilatant Thixotropic Rheopectic Bingham body Described as Power Law fluids as behaviour defined by τ= K(γ) n Where K is a consistancy index (Pa.s n ) And n is a dimensionless flow behaviour index n<1 = pseudoplastic n=1 Newtonian n>1 =dilatent
Pseudoplastic Flow Shear Stress Shear Thinning Viscosity drops with increasing shear rate Often due to interactions in constituents in complex fluids May trend towards Newtonian behaviour as shear rate increases No single figure for viscosity Apparent viscosity (η app ) is used, this is the viscosity at a specific shear rate and must be quoted with that shear rate. B A Shear rate For apparent viscosity at shear rate A, get associated value for shear stress and calculate viscosity at that point in the curve. η app = τ / γ (Pa.s)
Shear Stress Dilatant Flow Shear thickening behaviour Mostly observed in slurries with high solids loadings Especially where the level of the fluid approaches that where there is just enough to fill all the gaps between the particles when the slurry is at rest Rearrangement of particles within the slurry into less closely packed arrangements when the shear is applied. This increases the volume of space between the particles Results in there not being enough fluid in the system to allow for flow of the particles past one another. This leads to increased particle interactions and so the viscosity is seen to rise. Shear rate
App Viscosity Thixotropic Flow Closely related to pseudoplastic flow Fluids will often display both Both are shear thinning Defining factor with thixotropy is that it is time dependent Viscosity drops with time at a constant shear rate Generally will trend to a steady value as system equilibrates Can also be seem as a hysteresis on shear stress-shear rate curve Larger hysteresis more thixotopy Particle crowding and polymer chain interaction can lead to thixotropy Increase in shear rate As shear is applied it takes time for particles to begin to move uniformly throughout the slurry Similarly polymer chains can induce thixotropy as they take time to align to the flow Breakdown in structure between binder and particles Time Flocculated systems can exhibit thixotropy. Flocs contain interstitial spaces which can trap solvent As shear is applied flocs break apart releasing solvent so dropping viscosity System will reach steady state. If shear is increased further more strongly bonded flocs may then disperse This again will show another drop Platelets can also show this form of flow behaviour. At rest platelets are randomly orientated As shear is applied they will with time become aligned to the flow They will then slip past one another with lower resistance
Shear Stress (Pa) Yield Yield is the minimum applied shear before flow will take place If the post yield flow is Newtonian fluid behaviour is termed a Bingham body τ = τ y + ηγ Non-Newtonian τ = τ y + K(γ) n (Herschel-Bulkley Model) Yield stress is determined by extrapolation of the curve back to 0s -1 By plotting τ against γ should give a straight line Casson Model τ ½ = τ ½ y + K(γ) ½ Only an approximation, Not all pseudoplastic materials will follow -more so at low shear rates Yield Shear Rate (s -1 ) Caused by interactions between slurry constituents Binder Particle Surface adsorption Binder- Binder Polymer chain length Polymer chain geometry (bulky side groups) Binder Solvent How well has chain dissolved Chain mobility in solvent (bond rotation) Formation of longer range structure in the slurry body Can form Gel type structures Often accompanied with thixotropic behaviour Takes time for structures to break down then reform
Viscosity Measurement Most common method by rotational viscometer (Brookfield) Viscosity is measured as a resistance to the rotation (Torque) Cup & Bob and Cone & Plate are 2 common variations ω θ<4 c r Cup & bob good for fast drying slips due to small area for evaporation. Calculation does not take into account effect of viscosity gradient under bob. Cone and plate better for trying to gain more absolute and uniform values of shear stress and rate. Shear rate is related to rotational speed and gap width at any point on r. Shear stress = T/⅔πr 3 shear rate= ω/sinθ Cone & plate best suited to slow drying pastes and inks
Important Considerations in Viscosity Measurement Temperature Control Pastes and slurries very sensitive to temperature, use of system with controlled temperature water bath recommended History of sample any shear applied to sample will affect measured result, especially if it is thixortopic, Minimise disturbance, follow set procedure with controlled delays Be aware of effects of solvent evaporation in volatile specimens, may affect viscosity over time (also skin formation)
Other characterisations to Consider Weight loss and shrinkage on drying Mechanical tests green strength, flex, tear resistance, surface roughness Burn out characteristics TGA, Dilatometry Firing shrinkages Important if making multilayer devices as these must be matched carefully.