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## Seminar Basics of Rheology - Oscillation

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**SeminarBasics of Rheology - Oscillation**Markus Nemeth very welcome !**Introduction Viscoelastic Behavior**Using a simple illustrative picture: „The Rheology Road“ viscous viscoelastic elastic ideally viscous liquids such as water, oils Law of Newton viscoelastic liquids such as glues, shampoos viscoelastic solids such as pastes, gels, rubbers ideally elastic (rigid)solids such as stone, steel Law of Hooke rotational tests | oscillatory tests • e-learning(Eiffel tower)**IntroductionViscoelastic Behavior**tack (showing long strings), e.g. of adhesives, printing inks, or food (mouth sensation) stirring process: " Weissenberg effect " (rod climbing effect), poor mixing result(Karl Weissenberg, 1893 to 1976, rheologist) extrusion: extrudate swelling, e.g. dimension stability Result: In many cases, the measurement of viscosity only is not sufficient since elastic effects are occurring, resulting in viscoelastic behavior.**IntroductionViscoelastic Behavior**polymers polymer solutions(here: poly-iso-butylene, PIB) die swell or extrude swell" Weissenberg effect " when flowing out of a capillary, when stirring a pipe or a bottle • Movie (PVA solution)**IntroductionViscoelastic Behavior**polymers polymer melts extrusion (e.g. polystyrene, PS):extrudate swellingand melt fracture blow moulding(e.g. polyethylene, PE):orange peel or shark skin**DefinitionsShear Stress, shear deformation or shear strain**The two-plates model = shear stress unit: 1 N / m2= 1 Pa (Pascal) shear deformationorshear strain = unit: 1 m / m = 1 = 100%**DefinitionsElasticity Law**spring Law: F / s = C spring force F deflection path s spring constant C (stiffness) definition of the shear modulus Robert Hooke (1635 to 1703) unit of the shear modulus: (1 Pa / 1 = ) 1 Pa further units: 1 GPa = 1000 MPa = 106 kPa = 109 Pa (Giga-pascal, Mega-pascal, kilo-pascal) • Movie (bouncing balls)**ApplicationShear Modulus**Material stiffness and shear moduli Example: different types of cheese 1 2 5 4 • e-learning (cheesemice)**DefinitionsTensile Tests (1)**for tensile tests: E - modulus, or Young's modulus (in Pa) s= tensile stress (in Pa) e= elongation (in 1 = 100%) E = 2 G (1 + ) with Poisson's ratiom For all kind of materials: E = (2 to 3)G**DefinitionsTensile Tests (2)**tensile stress / elongation diagram of a steel specimen with yield stress S, yield strength S, breaking stress B and elongation at break B Poisson's ratio l ... length,d ... thickness of the specimen l = l – l0change in length d = d0 – dchange in thickness clamp “plastic deformation“,lattice dislocation of crystals speci-men linear elastic deformation = E • force F**DefinitionsTensile Tests (3)**coatings polymers brittle fracture when T<Tg “cold flow“ when Tg-30°C to Tg “rubber-elastic“ when T>Tg Tg ...glass transitiontemperature tensile testson polymers or coating films being unlinked or showing a low degree of cross-linking**DefinitionsShear Rate, Deformation and Strain Rate**a) shear rate as the velocity gradient (for flowing fluids) b) shear rate as the time-dependent rate of deformation, or strain rate Explanation: As a summary, in the eyes of a rheologist for all kinds of materials counts: being a viscous solid or an elastic liquid – they all are viscoelastic.**Viscoelastic BehaviorYield Point (using a / -**Diagram) Yield point as the limiting value of the shear stress: The sample starts to flownot before the externalforces are exceeding thenetwork-of-forces of the internal structure. Below the yield point there is elastic deformation. Testing with controlled shear stress lg lg lg lg yield pointy using the best straight fitting line (“tangent“) in the linear-elastic deformation range yield pointy using the „tangent crossover“ method**106**% without a binderyield point 13.5 Pa 104 lgg with a binder yield point 114 Pa 102 100 10-2 Pa 0.1 1 10 100 1000 shear stress lg t Viscoelastic BehaviorYield Point (using a / - Diagram) food comparison of two ketchups deformation**600**Pa 400 t 200 0 0 20 40 60 80 100 s-1 shear rate Pa 100 lg t 10 1 0.1 0.001 0.01 0.1 1 10 s-1 100 shear rate lg Viscoelastic BehaviorYield Point (using Flow Curves) comparison of two coatings coatings 2 1 primer2 top coat 1 linearscale e.g. as 15 Pa at 0.01 s-1 2 1 logarithmicscale**%**• primer • without a yieldpoint • top coat • yieldpointy = 7.02 Pa (whenpresetting5% toleranceofdeviation) 104 103 102 101 100 10-1 Pa 0.01 0.1 1 10 100 shear stress lgt Viscoelastic BehaviorYield Point (using a / - Diagram) coatings Comparison of two Coatings Summary:The Top Coat (2)shows a yield point, the Primer (1)however does not. 1 lg g deformation 2**RheometryOscillatory Tests: Basics (1)**Two-Plates Model Ideally elastic behavior of a totally stiff sample(e.g. a stone, or steel): There is no shift betweenthe sine curves of shear strain (deformation) and shear stress : the curves of and are “in phase“ • Movie (2-plates-model, Ideally elastic behavior)**RheometryOscillatory Tests: Basics (2)**Preset: constant frequency and constant amplitude Result: Most samples are showing viscoelastic behavior with the phase shift between the sine curves of the test preset (here: strain) and the measuring result (then: stress), as retardation of the measuring response to the preset oscillation. It counts:0° 90° ideally elasticideally viscousbehavior • Movie (2-plates-model, visco-elastic behavior)**RheometryOscillatory Tests: Basics (3)**Elasticity law of Hooke(for oscillation): Index A for „Amplitude“ G* [Pa] complex shear modulus G' [Pa] storage modulus, elastic portionG'' [Pa] loss modulus, viscous portion of the viscoelastic behavior vector diagram Physically:G' for the stored and G'' for the lost (dissipated) deformation energy tan d [1]= G''/ G' loss factor or damping factor as the ratio between the viscous and elastic portion**IntroductionViscoelastic Behavior** viscous viscoelastic elastic with tand= G'' / G'**RheometryOscillatory Tests**Conversion of angle units (since degree is no SI unit): For in degrees or in rad (= 1000 mrad) holds: 360° corresponds to 2 rad(full circle) • e-learning (oscillation)**Rheometry (Oscillation)Amplitude Sweeps, preset**Preset: constant frequency (e.g. the angular frequency = 10rad/s or 10s-1) andvariable strain (deformation) Frequency Conversion:=2 f with angular frequency s-1 and frequency f Hz(since Hz is not an SI unit !) • Movie (amplitude sweep)**Viscoelastic Behavior Amplitude Sweeps**Limiting valueof the LVE - range Result: storage modulus G' (elastic behavior),loss modulus G'' (viscous behavior),limiting value of the linear viscoelastic (LVE- ) range when reaching L - at the given test conditions, i.e., at the preset (angular) frequency - left side: G‘ > G‘‘ (“gel-like structure“) in the LVE - range right side: G‘‘ > G‘ (“liquid structure“) in the LVE - range**Viscoelastic Behavior Amplitude Sweeps**polymers 105 Pa polymer melt lg G' viscoelastic liquid, liquid character since G‘‘ > G‘ 104 lg G'' limit of the LVE range at= 10% = 0.1 ω = 10 rad/sT = +180°C 103 -2 -1 0 1 2 3 10 10 10 10 10 % 10 strain lg g**Viscoelastic Behavior Amplitude Sweeps**polymers dispersions 1000 kPa sealant 100 paste-like, viscoelastic gel-like character in the LVE range since G‘ > G‘‘ lgG' 10 lg G'' Limit of the LVE-range at = 0.026% = 2.6 10-4(with 10% tolerance of deviation) 1 ω = 10 rad/sT = +25°C 0.1 0.001 0.01 0.1 1 10 % 100 strain lg g**Viscoelastic Behavior Amplitude Sweeps**coatings comparison of two spray coatings 10 coat 1: G' > G'' Pa spray coat 1 showing levelling problems spray coat 2 showing good levelling coat 2: G'' > G' in the LVE range lgG' 1 lg G'' ω = 10 rad/sT = +25°C 0.1 1 10 100 % 1000 strain lg g**100**Pa 10 1 0.1 % ω = 10 rad/sT = +23°C 0.01 0.1 1 10 100 1000 Viscoelastic Behavior Amplitude Sweeps coatings comparison of two coatings top coat: G' > G'' primer top coating lgG' primer: G'' > G'in the LVE range lg G'' strain lg g**Viscoelastic BehaviorAmplitude Sweeps**food temperature dependence of butter 10 MPa T = +10°C 1 Summary: cold butter shows brittle break,hence poor spreadability lgG' 0.1 lg G'' T = +23°C 0.01 ω = 10 rad/s 0.01 0.1 1 % 10 strain lg g**Viscoelastic Behavior Amplitude Sweeps**food Gel strength, dependence on the binder - concentration 10,000 15 w-% Pa starch gel (in water) 10 w-% 1000 Summary: The gel strengthis dependent on the binder concentration lgG' 7.5 w-% 5% w-% 100 10 ω = 10 rad/sT = +23°C loss factor tan = G‘‘ / G‘ First check in the LVE range: tan < 1 for all samples ( = gel structure) ? Yes ! lg tand 1 0.1 0.1 10 % 100 1 strain lg g**Viscoelastic BehaviorAmplitude Sweeps**food comparison of two starch gels 1000 native corn starch modified corn starch Pa lgG' • native, unmodified • starch shows brittle break, • hence poorproportioning 100 lg G'' (2) G‘‘- maximum indicates: - a network of the superstructure - microcracks before breaking ω = 10 rad/sT = +23°C 10 0.01 0.1 1 10 100 % 1000 strain lg g**Viscoelastic Behavior**exceeding the LVE range ...**Viscoelastic Behavior Amplitude Sweeps**mineral oils comparison: basic oils for lubricating greases, at T = +20 and -40°C 106 Oil 1 at -40°C: inhomogeneous, showing G’ = G’’ Oil 1: partially syntheticOil 2: fully synthetic Pa Oil 1 (+20°C) (G' = 0) Oil 2 (+20°C) (G' = 0) Oil 1 (–40°C) (pourpoint -24°C, now pulp - like) Oil 2 (–40°C) (G' = 0) (pourpoint -60°C, hence still liquid) lgG' 104 Oil 2 at -40°C: ideally viscous (no elastic portion: G’ = 0) 103 lg G'' 102 both oils at +20°C: ideally viscous (no elastic portion) 101 100 0.01 0.1 1 10 % 100 strain lg g**Viscoelastic Behavior Amplitude Sweeps**Analysis of the yield point and flow point here: functions of G' and G'', and theshear stresst on the x - axis lg G‘ lg G‘ lg G‘‘ lg G‘‘ yield point:t - value at the limit of the LVE-range,flow point:t - value at the crossover point, when G‘ = G‘‘at the given test conditions, i.e. at the preset (angular) frequency**Viscoelastic Behavior Amplitude Sweeps, Flow Point**cosmetics comparison of two tooth pastes, flow points 10,000 Pa 1000 lg G' paste 1 flow point: f = 125 Pa paste 2 flow point: f = 24.9 Pa lg G'' 100 10 1 10 100 1.000 0.01 0.01 0.1 Pa • e-learning (toothpastes 1 & 2) shear stress lg **Viscoelastic BehaviorEffect of Rheological**Additives(oscillation, amplitude sweeps) dispersions Example: comparison of a dispersion containing * additive 1, as a „gellant“ e.g.clay + additive 2, as a „viscosifier“ e.g. an associative thickener coatings 1 2 Summary for the LVE range: with the gellantG‘ > G‘‘(„gel - like structure“), with the viscosifierG‘‘ > G‘(liquid - like behavior), hence no form stability LVE range 1 G' > G'' lg G' lg G'' LVE range G'' > G' 2 shear stress lg gellant: yield stress at y = 6.9 Pa flow stress at f = 42 Pa**Viscoelastic Behavior Amplitude Sweeps, Flow Point**lube greases comparison of 3 lube greases, at T = +25 and –40°C flow stress F T = - 40°C upper 3 curves: T = - 40°C NLGI 2 (F= 10 kPa) NLGI 1 (F= 7 kPa) NLGI 0 (F= 5 kPa) lower 3 curves: T = + 25°C NLGI 2 (F= 400 Pa) NLGI 1 (F= 200 Pa) NLGI 0 (F= 100 Pa) consistency of lubrification greases according to theNLGI classification(National Lubrification GreaseInstitute in USA), using the cone penetration method (pen values) lg G' lg G'' T = + 25°C SEM image of a Li -soap grease shear stress lg **Rheometry (Oscillation)Frequency Sweeps, preset**Preset: constant amplitude, shear strain or shear stress (within the LVE - range)andvariable frequency Precondition: First of all, the LVE - range has to be checkedby performing an amplitude sweep. • Movie (frequency sweep)**5**10 Pa 4 4 10 10 Pas 3 10 2 3 10 10 1 10 -3 -2 -1 0 1 2 3 10 10 10 10 10 10 10 rad/s angular frequency lg w Viscoelastic Behavior Frequency Sweeps polymers typical behavior of an unlinked polymer 0 = 35kPas PDMS (poly - di - methyl - siloxane) lg G' lg G'' lg|h*| G > G crossover G > G g = 10%T = +23°C**Viscoelastic Behavior Frequency Sweeps**polymers unlinked polymers Maxwellian fluids are showing The position of the crossover pointthe slopes 1:1 and 2:1, respectively, of G' and G'' is depending on the of G''(w) and G'(w) averagemolar mass M in therange of low frequencies. (here: M1 > M2).**Viscoelastic Behavior Frequency Sweeps**polymers polymers showing different molar masses 106 polyethylenemelts PE 1 MFR = 0.30g/10min (melt flow rate) PE 2 MFR = 2.41 Pa 105 PE 1 lg G' 104 PE 2 lg G'' 103 g= 10%T = +180°C Summary:The average molar mass of PE 1 is greater. 10-2 10-1 100 101 102 103 rad/s angular frequency lg w**Simple Test MethodsMFR / MVR testers**polymers Single-point tests for polymers melts using a “low-pressure capillary viscometer“ according to ISO 1133. Result: MFR ... melt flow rate (in g / 10 min) or MVR ... melt volume flow rate (in cm³ / 10 min) Example: polyethylene PE at T = 190°C; weight 2.16kg polymer melt**Viscoelastic Behavior Frequency Sweeps**polymers unlinked polymersfunction of the complex viscosity * 0 It counts: * = G* / and G*² = G ² + G ² At low frequencies, Maxwellian fluids are showing the plateau of the zero-shear viscosity 0 . The value of 0 is proportional to the molar mass M(at the same polymer concentration). Formally:**Pa**4 10 3 10 2 10 -1 0 1 2 3 10 10 10 10 rad/s 10 Viscoelastic Behavior Frequency Sweeps polymers comparison of unlinked and cross-linked polymers polyethylenemelts unlinked crosslinked crosslinked: G' > G'' lg G' lg G'' unlinked: G'' > G' g= 1%T = +170°C angular frequency lg w**Viscoelastic Behavior Frequency Sweeps**polymers comparison of two resins Evaluation of the behavior-at-rest in the range of low frequencies Left: unlinked molecules since G'' > G' the |*|-function shows the plateau of the zero-shear viscosity 0 (thus, the behavior of a viscoelastic liquidat rest),Right: cross-linked molecules since G' > G'' the |*| function is rising towards an infinitely high value (thus, a “gel - like structure” with stability at rest).Comment: Specifications of |*| are not useful in the range of G' > G''.**10**Pa 0.1 0.001 -3 -2 -1 0 1 2 10 10 10 10 10 rad/s 10 Viscoelastic Behavior Frequency Sweeps comparison of two coatings: dispersion stability dispersions coatings coat 1: G' > G'' 1 Long - term storage stability: Evaluation at a low frequencyG' > G'' hence „gel-like“,stable dispersion (1, Top Coat ). G'' > G' hence „liquid“, unstable dispersion (2, Primer). lg G' lg G'' 0.01 g= 1%T = +23°C coat 2: G'' > G' angular frequency lg w**Viscoelastic Behavior Effect of Rheological Additives**(Oscillation, Frequency Sweeps) coatings dispersions Example: comparison of a dispersion containing * additive 1, as a „gellant“ e.g. clay, + additive 2, as a „viscosifier“ e.g. anassociative thickener 1 2 stable: G' > G'' Summary of the long-term behavior(see the range of low frequencies):with the gellantG‘ > G‘‘(a „gel-like structure“), hence stability,and with the viscosifierG‘‘ > G‘(liquid behavior), hence nosedimentation stability 1 lg G' unstable: G'' > G' lg G'' 2 angular frequency lg G‘ gellant G‘‘ gellant G‘ viscosifier G‘‘ viscosifier**Pa**3 10 2 10 1 10 -1 0 1 2 10 10 10 rad/s 10 Viscoelastic Behavior Frequency Sweeps cosmetics comparison of two cosmetic lotions: stability stable dispersion: gel-like with G' > G'' at low frequenciesunstable dispersion: liquid with G'' > G' at low frequencies D1 unstable lg G' lg G'' D2 stable g = 0.3%T = +20°C angular frequency lg w**ViscoelasticBehaviorComparison: Shearratesfor Rotation**andOscillation • Calculationofshearratesforoscillatorytests • =A • Unit: 100% (rad/s) = 1 (rad/s) = s-1 • ______________________________________________________________________________________________________________________ • Examples: • Amplitude sweepshear rate = 10% 10 rad/s = 0.1 10 rad/s = 1 s-1Withunlinked & unfilledpolymers in maximumupto 100 % 10 rad/s = 10 s-1 • 2) Frequencysweepshear rate = 1% 100 rad/s = 0.01 100 rad/s = 1 s-1 • Withunlinked & unfilledpolymersupto 10% 628 rad/s (or 100 Hz) = about 63 s-1 • _______________________________________________________________________________________________________________________ • Summary: Foroscillatorytests, theshearratesusuallyare in thelowshearrange.**Viscoelastic BehaviorTime - dependent Structure Recovery**Step test with 3 intervals, as an oscillatory test(measuring „thixotropic behavior“) preset: 1 low - shear conditions 2 high - shear conditions 3 low - shear conditions measuring result: 1 state of rest 2 structure decomposition 3 structure regeneration 2nd test interval:G‘‘ > G‘ (hence liquid at high shear)1st & 3rd test interval:G‘ > G‘‘(„gel-like structure“ at rest)**10**kPa 1 G' G' G'' 0.1 G'' 0 20 40 60 80 100 s 120 time t Viscoelastic BehaviorTime - dependent Structure Recovery adhesives dripping SMD adhesive step test: 3x Oscillation (for surface-mounted devices, e-technics) lg G' structure recovery lg G'' g1 = g3 = 0.2%g2= 100% ω = 10 rad/s T = +23°C Summary: continued dripping, since still G‘‘ > G‘