Overview of the lectures in polymer physics. Solid-State Properties

Transcription

1 Overview of the lectures in polymer physics Topics: The amorphous state The crystalline state Thermal transitions and properties Mechanical properties Rubber elasticity Polymer blends and IPNs Polymer composites and nanocomposites Polymer processing and rheology Lecurer: Patric Jannasch Institute of Chemistry, Division of Polymer & Materials Chemistry Solid-State Properties Different chain conformations in different phases Amorphous Dissordered, entangled state Semi-crystalline Partly ordered, partly folded state Increasing crystallinity PS PVC PE PMMA PP p

2 The Amorphous State spaghetti analogy Randomly coiled interpenetrating chains Entanglements at sufficiently high molecular weight Not all volume is occupied: free volume concept Diffusion of small molecules Segmental and chain mobility strongly dependent on temperature and free volume Amorphous high h molar mass polymers can be in the glassy state, rubbery state or melt state going from low to high temperature p. 154 Chain Entanglements Sufficiently long molecules Critical molecular weight Depend on chain flexibility Restrict flow M c critical molecular weight for formation of stable entanglements M e molecular weight between entanglements M c 2M e Flexible chains give high M c, aromatic main chains give low M c The molecular weight of commercial polymers significantly above M c p

3 Reptation model in the melt state How do polymers move in the entangled state? Theory of De Gennes long range movements of chains snakelike motion within a virtual tube frictional resistance by entanglements successful in predicting viscous properties of entangled polymer melts p. 156 The Glass Transition Different theories isoviscous state (10 12 Pa s) - isofree volume state -isoentropic state: conformational entropy goes to zero Free volume V f is the difference between actual volume V and occupied volume V 0. V f = V - V 0 The glass transition depends on - chain flexibility -interaction p

4 Secondary-Relaxation Processes Small scale molecular motions that occur in the glassy state: - Limited rotations in the main chains - Movements of side groups Important for glassy state properties (impact strength, gas permeation) Example: crankshaft motion 5 bonds rotate around the main chain p. 158 Summary low Temperature Mobility and free volume high Glassy state ---- Glass rubber transition ---- Rubbery state Melt state Small scale molecular motions - large scale segmental motions polymer chain reptation 4

5 The Crystalline state Many important polymers are partially crystalline Polyethylene Polypropylene Polyamides; Nylon 6, Nylon 6.6, Nylon 4.6 Linear polyesters; PET, PBT Crystallinity influences stiffness and brittleness fracture strength and elongation at break solubility permeability of gases and water sorption many other properties p. 158 Ordering of polymer chains High thermal energy favours a large number of conformations Lower-energy conformations are favoured during cooling Eventually the polymers are able to attain their lowest-energy conformation, often the extended chain or the planar zigzag (e.g., polyethylene, nylons) polymer helix folded polymer chain The lowest-energy conformation of syndiotactic polymers, and polymers with large substituents, is usually a helix (e.g., polypropylene, polyisobutylene) The packing of polymers in ordered structures is favoured by stereo regular symmetrical chain structures and specific interactions (tacticity, trans configuration, hydrogen bonding) 5

6 Crystalline structures Polymer crystallisation by chain folding folded polymer chain crystalline lamellae p. 158 Chain folding in lamellae Three idealized models for chain folding in lamellae A. Nonadjacent reentry B. Regular adjacent reentry C. Irregular adjacent reentry Lamellae thickness: nm (in PE repeating units) p

7 Thermal Transitions Hydrogen bonding between the amide groups in nylon 6.6 For many polymers T g is one-half to two thirds of the melting temperature T m ( in Kelvin ) p. 162 Crystalline-Melting Temperature Free energy of fusion per repeating unit: G u = H u T S u Equilibrium melting temperature at G u =0 (crystalline lamellae are destroyed as fast as they are formed) T m0 = H u / S u T m 0 >T m p

8 Crystallization Kinetics Linear growth rate of spherulites in PET T g = 69 o C, T m = 265 o C Thermodynamic driving force below T m m, and necessary mobility above T g Crystallisation possible between T g and T m Increasing viscosity at low temperatures Possible to quench polymers with slow crystallisation rates Avrami equation: the fractional crystallinity is = 1 exp(-kt n ) k is a temperature dependent parameter n varies between 1 and 4 depending on the nature of growth process p. 164 Techniques to Determine Crystallinity Non-destructive Density measurements: fractional crystallinity = ( a )/( c - a ) c from single crystals, a from quenched samples X-Ray diffraction (WAXS): weight fraction of crystalline phase W c = 1 I am / I am 0 HDPE Bragg peaks From thermal transitions Differential Scanning Calorimetry Dilatometry Amorphous halo p

9 Measurement Techniques - Dilatometry Principle: capillary bulb increasing T mercury polymer sample Specific volume as a function of temperature of a semicrystalline polymer Change in thermal expansion coefficient at T g : = l - g p. 173 Measurement Techniques - Differential Scanning Calorimetry (DSC) Principle S is sample and R is reference pan Individual heaters to keep T=0 during a temperature scan. Difference in the required heat flow is measured. DSC thermogram of PET glass transition near 75 o C recrystallization above 143 o C melting endotherm around 250 o C crystallinity = Q/ H f with Q the heat of fusion measured and H f the heat of fusion at 100% crystallinity p

10 Other Measurement Techniques Many properties change drastically at the glass transition temperature and can be used to determine T g such as: Mechanical properties Dielectric properties Optical properties load pressure Temperature at 0.25 mm deflection = HDT p. 177 Structure-Property Relationships Influence of flexibility of the polymer chain on the melting temperature for an analogous series of polyesters T m0 governed by S u. Flexible polymers have higher S u T m0 = H u / S u p

11 Structure-Property Relationships Influence of hindered chain rotation of the polymer chain on the glass-transition temperatures of selected vinyl polymers O O O flexible polymer O inceased polarity rod polymer R R R' R' ladder polymer p. 179 Structure-Property Relationships Effect of increasing size of the substituent groups on the glass-transition temperature of polymethacrylates Increasing flexibility of the side chain Influence by tacticity i-pmma, Tg = 45 o C a-pmma, Tg = 105 o C s-pmma, Tg = 115 o C p

12 Effect of molecular weight on T g The glass transition temperature is dependent on the number average molecular weight The effect levels off at high M n Fox-Flory equation: T g = T g K/M n in Kelvin The constant K is polymer-specific The effect can be related to the free volume contribution of chain ends. p. 180 Effect of composition on T g The glass transition temperature of a homogeneous mixture is dependent on the amount of each component present, and their respective T g. Rule of mixtures: T g = W 1 T g,1 + W 2 T g,2 Fox equation: 1/T g = W 1 / T g1 g,1 + W 2 / T g2 g,2 p

13 Mechanical Properties How are polymers deformed? - mechanisms of deformation At small deformations: elastic, viscous, viscoelastic time dependent, frequency dependent At large deformations: crazing shear banding fracture p. 183 Crazing Crazes consist of polymer microfibrils ( nm in diameter) bridging two surfaces of a crack. Crazes develop at a certain critical strain True cracks appear after degradation of crazes direction of deformation craze propagation p

14 Crazing Crazes in a polycarbonate dogbone Crazes in poly(phenylene oxide) p. 184 Shear banding Shear banding: - occurs in some glassy amorphous polymers instead of, or together with, crazing. - is the dominant mode of deformation of ductile polymers during tensile testing - provides larger energy dissipation in, e.g., polycarbonate and SAN p

15 Stiffness and Strength Methods of testing In tension, shear or hydrostatic static: deformation rate is constant transient: creep and stress relaxation impact: Izod and Charpy cyclic: fatigue p. 186 Static tensile testing Dogbone sample engineering (nominal) stress = F/A 0 engineering (nominal) strain = L / L 0 Alternatively: true stress and true strain true stress T = F/A actual cross section A true strain T = ln (L/L 0 ) p

16 Static tensile testing During uniaxial tensile deformation, glassy amorphous polymers increase in volume V. V = V V 0 = ( 1-2 V 0 V 0 is the initial (unstrained) volume is the true strain is Poisson s ratio, defined as the ratio of true strain in transvers direction and true strain in longitudinal direction. = - trans / axial = - x / y p. 187 Poisson s Ratio Molecular origin: strain contacted relaxed extended = - trans / axial For the majority of polymers 0.4 Incompressible polymers have = 0.5 p

17 Static testing Determination of materials properties in tension Hooke s law = E linear elastic behaviour = stress, E = tensile modulus, = strain Alternatively: = D D = 1/E = tensile compliance In reality: effects of time, rate and temperature p. 189 Modulus as a function of temperature Glassy modulus typically 1 GPa Rubbery plateau modulus typically 1 MPa Entanglements responsible for rubbery plateau (physical crosslinks) Chemical crosslinks have the same effect The rubbery plateau modulus E p is inversely proportional to the molecular l mass between entanglements M e E p proportional to RT/M e p

18 Materials properties in shear Engineering (nominal) shear stress, = F/A 0 Shear strain, = tan = X/C Hooke s law: = G G = shear modulus = J J = 1/G = shear compliance p. 191 Stress-strain as a function of temperature x marks the stress and strain at failure y 1. Brittle low temperature behaviour 2. Ductile behaviour with yield stress 3. Ductile behaviour with yield stress, necking, cold drawing and orientation hardening 4. Rubbery behaviour with strain-induced crystallisation p

19 Necking of ductile polymers Simulation of the development of a neck via shear banding Effective plastic strain A polyethylene sample with a stable neck Mechanism for the deformation of a semicrystalline polymer (a) Two adjacent chain folded lamellae and interlamellar amorphous material before deformation (e) Orientation of the block segments and tie chains with the tensile axis in the final deformation stage (d) Separation of the crystalline block segments during the third stage (b) Elongation of amorphous tie chains during the first stage of deformation (c) Tilting of lamellar chain folds during the second stage 19

20 F 0 F 0 Mechanical properties of representative polymers Tensile response depends on: - polymer structure and architecture - MW and MW distribution - sample preparation - crystallinity - temperature - rate of deformation p. 194 Time dependent behaviour: creep Creep : constant stress 0 and measuring the time dependent strain (t) Result: compliance D(t) = (t)/ 0 Important t for polymers that t must sustain loads for long periods (0) t (t ) =D 0 p

21 Time dependent behaviour: stress relaxation Stress relaxation : constant strain 0 and measuring the time dependent relaxing stress (t) Result: modulus E(t) = (t) / 0 t 0 0 (0) (t ) (0) 0 0 t p. 196 Stress and strain Static tensile testing: constant strain rate Observe how the stress varies with the strain F(t) d dt = const. Creep testing: constant stress Observe how the strain varies with time (t) F 0 Stress relaxation: constant strain Observe how the stress varies with time 0 (t) 21

22 Relations between moduli and compliances Modulus in tension E Compliance in tension D Modulus in shear G Compliance in shear J Bulk modulus in compression K For isotropic materials two independent material properties E = 2(1+ )G J = 2(1+ )D K = E/3(1-2 ) With Poisson s ratio = 0.5 E = 3G J =3D K =infinite (incompressible) p. 192 Impact and fatigue testing Measures energy expended up to failure under conditions of rapid loading Impact strength critical in many applications Fatigue testing Oscillative stress p

23 Rubber elasticity p. 249 Chain conformations and entropy Which dynamic chain has the highest (conformational) entropy, S? a) b) c) S = k lnw d) 23

24 Rubber elasticity the Gough-Joule effect elongation Unloaded coiled chains in an entropically favoured dissordered state A rubber band acts like an entropy spring Stretched chains in a less entropically favoured state heating Stretched chains with a more entropically favoured state Rubber elasticity - models Elastic force = f = G 0 ( - = L/L 0 = 1 + G 0 = shear modulus, proportional to T and the crosslink density - Good fit at low - Overestimation at moderate because of deviation from Gaussian distribution - Underestimation at high because of strain-induced crystallisation Fillers in rubbers: Guth-Smallwood equation E f /E 0 = f f p