POLYMER RHEOLOGY - VISCOSITY BEHAVIOR AND FLOW TYPES
BASIC QUANTITIES STRESS - = F/A STRAIN - = dX/dY STRAIN RATE - ' = dVx/dY
VISCOSITY - = /' ENERGY DISSIPATION RATE (energy/vol*time) - ' = '2 The strain rate below is given as if the fluid is in shear, which is only one type of flow. Refer to schematic below.
Why is rheological behavior of polymer melts and solutions important:
(a) Can relate viscosity to MWs (b) Can relate viscosity to thermo. properties such as volumetric behavior but most important: (c) Must understand in order to process polymer melts, solutions.
Typical ' in processing: compression molding - 1-10 s-1 calendering - 10-102 s-1 extrusion - 102 -103 s-1 100 and above generally injection molding - 103 -104 s-1 out of Newtonian range
EXTRUDER - CYLINDRICAL DIE
The end of the screw contains a mixing element.
Stages of Injection Molding - (1) Retract and refill; (2) Soak (usually longest t; (3) Shot; (4) Hold t; (5) Gate freezes; (6) Piston retracts; (7) Ejection Typical Problems - (1) Weld lines (where 2 melting fronts meet); (2) Warpage (due to elastic stresses); (3) Incomplete freezing.
The mold entrance (sprue) is at top. TYPICAL BEHAVIOR - MELTS AND CONCENTRATED SOLUTIONS
Materials with broad MWD relax at lower ', and the relaxation region is broader. Short branches - below entanglement MWs - will lead to behavior similar to linear polymers (e.g., LLDPE).
Zero Shear scales with MW.
The transition is the entanglement MW. Power is 1 below transition; 3.4 above, i.e., = K [MW]3.4. Entanglemet transition also seen in solutions (below).
Below MWe polymers show less elastic behavior, wider Newtonian range, small "extra" normal stresses upon shearing. Under certain conditions the polymer can behave as Newtonian (constant ) at both low and high shear rates. For high MW, shear-induced chain degradation can take place first - e.g. - rupture of red blood cells.
This shear-thinning viscosity behavior results from coil-like behavior of most polymer fluids. The coils rotate under shear, causing disentanglement / entanglement with neighbors. This means high at low '. As ' increases, the coils rotate too fast to re-entangle, so /' decreases. Some energy stored by coils elastically - e.g., coils can elongate.
Elasticity is an important characteristic of polymer flows - observed as:
(1) Die Swell - polymer exits a die; elastic energy released perpendicular and parallel to flow; polymer expands shape.
(2) Rod Climbing - a Newtonian fluid spun by an agitator will form a vortex; a polymer will expand upward and climb the shaft.
(3) Transient Effects on Fluid Behavior - Upon acceleration, polymer may behave as a viscous fluid at short relaxation times, become viscoelastic at longer relaxation times / higher ', then finally become elastic at low strains and high shear rates or long relaxation times. At these conditions, the polymer deformation is in phase with applied stress.
What factors determine characteristic relaxation time of a polymer? Standard measure of elasticity - first normal stress coefficient, zero for purely viscous fluid. 2 12 = (11 - 22)/(') where 1 = principal flow direction; 2 = perpendicular For most polymers 12 is a function of ', similar in behavior to ELONGATIONAL FLOWS E.G. - (a) fiber spinning; (b) fiber drawing; (c) film blowing
MELT SPINNER Draw ratio = take - up rate / extrusion rate --- typically 10-100
- Get uniaxial orientation
FIBER DRAWING FIBER SHAPES - (a) cylindrical; (b) quadrilobal (gives less packing density)
- lower T to lock in orientation
- flow is not rotational as in shear - no variations perpendicular to flow
Wet Spinning - spin into bath to cause coagulation (e.g., rayon manufacture)
Dry Spinning - spin into "gas bath"
Blow up ratio - bubble D/die D - typically 1.5-4
- Get biaxial orientation
- Want to control "frost line" for semi-cryst. materials - An elongational flow is one where the strain rate = dVx/dX is the important deformation. The ratio between the stresses developed and the shear rate is the elongational viscosity. e = (11 - 22) / ' - why are both stresses important?
- This is a generic curve; dilution with solvent stretches it to right.
- In most molding operations, too much strain hardening undesirable, because the material relaxes slowly relative to molding rate; this causes warpage of final product. This is especially true of thermosets and thermoplastics with high MW tails. CONSTANT STRAIN RATE REQUIRES AN EXPONENTIAL INCREASE IN FLUID VELOCITY d = L/L d / dt = (1/L) (L/t) So if d/dt = ' = constant, then:
' = d(ln L)/dt ln(L / Lo) = o' t = Henke strain
Note: L increases exponentially with time.
Elastic stresses also cause problems with contracting, expanding flows - to the point of instability - the swirling leads to intermittent flow. The Deborah number (De) in caption is = characteristic relax. time / characteristic experimental time
[for example, texp might be the residence time in a die; trelax might be otained in a creep or strain recovery test.
A high De fluid is more elastic, more prone to flow instabilities (intermittent flows).