Professional products C9 opt : optimalisation, oral poster presentation C9 pfys : Oral presentation physical chemistry of polymers C9 Vscr : written literature review C9 Vpol : Research report ‘’from monomer to polymer C9 Pi : practical skills C9 IPV : individual project skills Overview
Deepening your prior-knowledge Higher Information density Code ORGFYC TOETS 02 Written exam POLYMER SCIENCE 3 rd year
Topics Rheology , introduction and modeling Forecast rheological properties with a simple model Thermodynamics of polymer mixing Effect of polymer mixing on thermal properties mechanical properties resulting morphology Addition of fillers and reinforcement with fibers and fabrics ( composites ) Polymer processing, injection molding
Introduction Some more examples before we start with POLYMER SCIENCE part 3
Todays ’ Learning objectives The principles of visco -elasticity in relation to viscosity Basic calculations on solid polymers
Rheology Amorphous polymers start to show displacement under a shearforce provided there is enough freedom of movement , otherwise displacement Rheology is the science of flow and deformation This Photo by Unknown Author is licensed under CC BY
Rheology is widespread ! http://www.economist.com/blogs/babbage/2011/11/rheology
Rheology If a force is removed suddenly of a short time the polymer will spring back to its original state: relaxation If the force is applied for a longer time flow will occur http://cit.kuleuven.be/smart/bgr 24-3-2013
Shear of a bar http://www.tulane.edu/~sanelson/Natural_Disasters/eqcauses.htm 24-3-2013 F
Important formulas Shear stress Shear strain Y X http://www.tulane.edu/~sanelson/Natural_Disasters/eqcauses.htm 24-3-2013
Important formulas Shear Modulus ( resistance against shear ) Shear rate (or gradient )
Hooke’s law Ideal solid: stress σ is proportional to deformation The proportional constant is E, Elasticity modulus Stress = Elasticity modulus *deformation σ = E ε
E moduli of some materials Material (at room temperature) E ( GPa ) Elastomers 0.001 - 0.1 Thermoplastic polymers 1 - 4 Thermosets 3-5 Ice (at - 4°C) 9.9 Ceramics 40 – 80 Glass 70 Aluminum 72 Steel 210 Diamond 1200
Example of an E modulus calculation A force F of 2.5 kN is applied to a round rod with a diameter of 1 cm and a length of 10 cm. The extension is 1 mm. Calculate the E modulus of this plastic? Which category? And a square rod of 1x1 cm...? F
Visco -elasticity When tension is removed from a liquid polymer, the material will partially return to its original state. The material is partially permanently deformed, viscous behavior The material has partially returned, elastic behavior. Visco elastic behaviour
Model for elastic behaviour A spring Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 100
Shear rate d γ / dt Two plates moving over each other at a speed v, this requires a force F h Force F speed V area A
Newton’s law Ideal liquid: stress σ is proportional to deformation rate d ε / dt . The proportional constant is η , the viscosity stress = viscosity*deformation rate σ = η d ε / dt
Model for viscous behaviour a dashpot Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 100
Viscosity of some materials Material (20°C) Viscosiy [ Pa.S ] Gas / air 10 -5 - 2*10 -5 / 1.8*10 -5 Acetone 3.2*10 -4 Water 10 -3 Ethanol 1.2*10 -3 Sulfuric acid 2.5*10 -2 Olive oil 10 -1 Glycerine 1.48 Honey 10 Polymer melts 10 - 10 4
Exercize Show a combination of a dashpot with a spring and describe the behavior in a stress strain diagram http://project-middle-grade-mayhem.blogspot.nl/2013/01/writing-advice.html
Let’s continue Basic models for polymer smelts and solid polymer (Maxwell, Kelvin-Voigt, Maxell Wiechert and Burgers) Simple approach of strain vs time diagrams for these models
Combinations Maxwell Kelvin Voigt Maxwell Wiechert Burgers All descibe response on external load
Maxwell model Response on external load spring dashpot Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 101
An example A stress of 2 MPa is applied to a Maxwell element for 20 seconds. The elastic modulus belonging to the elastic part is 0.5 GPa and the viscosity of the viscous part is 2 *10 10 Pa.s . Calculate the total strain of the system. 0.004+0.002 = 0.006 or 0.6%
Maxwell model, relaxation After removing the load, the internal tension slowly relaxes, relaxation...... Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 101
Maxwell Wiechert model Allows multiple relaxation times to be described via parallel-connected Maxwell models having a range of E moduli and viscosities More realistic Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 105
Kelvin- Voigt model No instantaneous deformation, after removal of the stress the shape recovery proceeds via an asymptote Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 103
Assignment Draw the stress onto a maxwell element as a function of time, applying a constant strain at t1 and removing it at t2. Response ε σ t1 t2 t1 t2
Flow and creep How to describe these two aspects? We have a Maxwell model We have a Kelvin-Voight model
Properties of both models Maxwell: describes stress relaxation and irreversible flow Kelvin Voigt: Describes creep, with no instantaneous deformation and no stress relaxation Solution: combination of both models; the Burgers model
Burgers model Description of creep Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 103
Burgers model Describes Spontaneous elastic deformation Delayed elastic deformation or reversible creep Irreversible creep (flow) Still too simple to describe polymer behavior Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 103
Practical characterisation Creep, relaxation experiments lasting for 10 sec to years Visco-elastic behaviour using cyclic loading (next week) 10 -8 10 -4 1 10 4 Creep Dynamic measurements Eigen res . freq . sonic waves
Time temperature superposition Time temperature superposition , measurements at various temperatures , compiling a mastercurve For semi crystalline polymers only ! http://www.open.edu/openlearn/ocw/pluginfile.php/75528/mod_oucontent/oucontent/640/89ef48a0/f42d9f37/t838_1_047i.jpg 08-11-2016
Aging Physical aging slows the creep rate Caused by decreasing free volume in glassy polymers Means experimental results give a too pessimistic picture
Molecular background Time temperature relationship is very similar to the temperature dependence seen earlier. E(log t) gives the same as E(Temp) Glass-rubber, rubber-liquid transition E(Temp) easily measured with a DMTA
Dynamic load What does that mean? How to measure? Example from everyday life?
Some examples Dynamic load in daily practise http://www.ad.nl/ad/nl/1841/De-Autospecialist/article/detail/1963813/2010/02/02/Hoe-onstaat-het-geluidsverschil-in-autobanden.dhtml 26-3-1013 http://www.sporthuishelling.nl/prod.php?prod=1625 26-3-2013
Dynamic load Periodical deformation of an ideal elastic material
The response is in phase with the cyclic load IOP Conf. Series: Materials Science and Engineering 10 (2010) 012114 doi:10.1088/1757-899X/10/1/012114 Dynamic load
Periodic deformation of an ideal viscous material Dynamic load
IOP Conf. Series: Materials Science and Engineering 10 (2010) 012114 doi:10.1088/1757-899X/10/1/012114 Dynamic load The response is out of phase with the cyclic load
In reality the bevavior is somewhere between both extremes, δ between and ½ π amplitude in fase uit fase Dynamic load
Two E moduli can be distinguished In phase Out of phase Loss angle Dynamic load
E’ E’’ L.Sissler et al. Viscoelastic modelling of tennis ball properties , IOP Conf. Series: Materials Science and Engineering 10 (2010) 012114 doi:10.1088/1757-899X/10/1/012114 IOP Conf. Series: Materials Science and Engineering 10 (2010) 012114 doi:10.1088/1757-899X/10/1/012114 Dynamic load
Measurement of gelpoint during curing E' describes the elastic component (= solid) E’’ describes the viscous component (= liquid) During curing, the liquid monomer is reacting into a solid polymeric substance E' / E'' crossover during curing = gel point Usually in industry G' / G'' Relationship between E and G: E = 2G(1+ ν) ν is the contraction coefficient (0.5 for rubbers)
Curing of epoxy resin https://www.azom.com/article.aspx?ArticleID=12103 19-11-2019
Application for tires Damping curve of a rubber vulcanisate Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 128 Heat generation
Grip higher: how to influence? Tg shift towards higher temperature Tg of SBR is - 65ºC, mixing with styrene shifts Tg to higher values (Tg of PS is 95ºC) Application for tires
Tire A adapted to tire B Polymeren van keten tot kunststof , A.K.van der Vegt , Delftse Uitgevers Maatschappij (1994) pp 129 Tg shift Reduction of loose ends Heat dissipation reduced Grip increased
Reduce number of loose chain ends to have limited heat generation Consider how that can be done on a molecular scale ? Higher molar mass Smaller molecular mass distribution Chains without branching Terminal groups with some interaction Terminal groups that react specifically with sulfur Application for tires