Solid State Properties Chapter 4

Amorphous Glassy Semi-Crystalline Elastomeric Polyisoprene T g = -73 °C Polybutadiene, T g = -85 °C Polychloroprene, T g = -50 °C Polyisobutylene, T g = -70 °C Viscous Liquid Polymer Phases Polystyrene T g = 100 °C Polymethyl methacrylate, T g = 105 °C Nylon 6,6, T g = 50 °C; T m = 265 °C Poly ethylene terephthalate, T g = 65 °C; T m =270 °C Polydimethylsiloxane T g = -123°C; T m = -40 °C

Glass-rubber-liquid Amorphous plastics have a complex thermal profile with 3 typical states: Log(stiffness) Pa Temperature Glass phase (hard plastic) Rubber phase (elastomer) Liquid Leathery phase Polystyrene TgTg Tygon (plasticized PVC) PDMS polyisobutylene

Phase diagram for semi-crystalline polymer

Temperature TgTg TmTm TbTb Volume Glassy Solid Crystalline Solid Glassy Solids Polystyrene T g 100 °C PMMA T g 105 °C Polycarbonate T g 145 °C Rubber T g -73 °C Crystalline Solids Polyethylene T m 140 °C Polypropylene T m 160 °C Nylon 6,6 T m 270 °C Polymers don’t exist in gas state; RT for boiling is higher than bond energies Liquid Liquids Injection molding & extrusion Polydimethylsiloxane T m -40 °C Polymer Phases

Differential Scanning Calorimetry (DSC)

Modulus versus temperature

Viscous Response of Newtonian Liquids A A y F xx There is a velocity gradient (v/y) normal to the area. The viscosity  relates the shear stress,  s, to the velocity gradient. The viscosity can thus be seen to relate the shear stress to the shear rate: The top plane moves at a constant velocity, v, in response to a shear stress: v  has S.I. units of Pa s. The shear strain increases by a constant amount over a time interval, allowing us to define a strain rate: Units of s -1

Measuring viscosities Requires standards ,000 cP 1 pascal second = 10 poise = 1,000 millipascal second

Viscosity of Polymer Melts Poly(butylene terephthalate) at 285 ºC For comparison:  for water is Pa s at room temperature. Shear thinning behaviour

Scaling of Viscosity:  ~ N 3.4  ~  T G P  ~ N 3.4 N 0 ~ N 3.4 Universal behaviour for linear polymer melts Applies for higher N: N>N C Why? Data shifted for clarity! G.Strobl, The Physics of Polymers, p Viscosity is shear-strain rate dependent. Usually measure in the limit of a low shear rate:  o

Concept of “Chain” Entanglements If the molecules are sufficient long (N >100 - corresponding to the entanglement mol. wt., M e ), they will entangle with each other. Each molecule is confined within a dynamic “tube”. Tube G.Strobl, The Physics of Polymers, p. 283

Network of Entanglements There is a direct analogy between chemical crosslinks in rubbers and “physical” crosslinks that are created by the entanglements. The physical entanglements can support stress (for short periods up to a time  T ), creating a “transient” network.

An Analogy! There are obvious similarities between a collection of snakes and the entangled polymer chains in a melt. The source of continual motion on the molecular level is thermal energy, of course.

“Memory” of Previous State Poly(styrene) T g ~ 100 °C

Development of Reptation Scaling Theory Sir Sam Edwards (Cambridge) devised tube models and predictions of the shear relaxation modulus. In 1991, de Gennes was awarded the Nobel Prize for Physics. Pierre de Gennes (Paris) developed the concept of polymer reptation and derived scaling relationships.

There once was a theorist from France who wondered how molecules dance. “They’re like snakes,” he observed, “As they follow a curve, the large ones Can hardly advance.” D ~ M -2 P.G. de Gennes Scaling Concepts in Polymer Physics Cornell University Press, 1979 de Gennes

Entanglement Molecular Weights, M e, for Various Polymers Poly(ethylene)1,250 Poly(butadiene)1,700 Poly(vinyl acetate)6,900 Poly(dimethyl siloxane)8,100 Poly(styrene)19,000 M e (g/mole)

Amorphous Glasses (< Tg) T g : 40 carbons in backbone Starting moving in concert

Glass transition temperature

Rate of cooling affects Tg

Polymer T g ( °C)

Polymer T g ( °C)

Factors that affect Tg Polar groups increase packing density; more thermal energy is needed to created volume

Factors that affect T g Other polar vinyl polymer:

Factors that affect Tg

Main chain stiffness: reduced flexibility

Polyarylenes

Nylons or polyamides

Side Chain Rigidity Long chains plasticize Factors that affect Tg Anchors to movement

Long chains plasticize movements

Factors that affect Tg poly(methyl methacrylate)

Factors that affect Tg Tacticity

Factors that affect Tg Symmetry of substituents asymmetric symmetric Asymmetric have higher Tg’s

Factors that affect Tg: Mw

Factors that affect Tg: Crosslinking

Factors that affect Tg: Plasticizer Phthalates

Immiscible (Two phase) and miscible (blends) polymers

Tg as a function of film thickness

Glass Transition Rigid group in backbone Flexible polymer backbone Steric Hinderance Long plasticizing side groups Symmetrical substituents Polar functionalities Plasticizers

Additional Kinds of Transitions

Amorphous Polymers Thermo-mechanical properties