1. Solid State Properties
Chapter 4
Solid State Properties

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

3. Glass phase (hard plastic)
Glass-rubber-liquid
Amorphous plastics have a complex thermal profile with 3 typical states:
Glass phase (hard plastic)
Polystyrene
Temperature 3 9 6 7 8 4 5
Leathery phase
Tygon (plasticized PVC)
Log(stiffness) Pa
Rubber phase (elastomer)
polyisobutylene Tg
Liquid
PDMS

4. Mechanical Properties

5. Heat Distortion Temperature
The maximum temperature at which a polymer can be used in rigid material applications is called the softening or heat distortion temperature (HDT).
A typical test (plastic sheeting) involves application of a static load, and heating at a rate of 2oC per min. The HDT is defined as the temperature at which the
elongation becomes 2%.
A: Rigid poly(vinyl chloride)
50 psi load.
B: Low-density poly(ethylene)
C: Poly(styrene-co-acrylonitrile)
25 psi load.
D: Cellulose acetate
(Plasticized) 25 psi load.

6. Transient Testing: Resilience of Cured Elastomers
Resilience tests reflect the ability of
an elastomeric compound to store
and return energy at a given
frequency and temperature.
Change of rebound
resilience (h/ho) with
temperature T for:
1. cis-poly(isoprene);
2. poly(isobutylene);
3. poly(chloroprene);
4. poly(methyl methacrylate).

7. Types of Polymers Polymer Family Tree Polyethylene 33% Vinyls 16%
Polypropylene
15%
PMMA
ABS
Nylon
Polycarbonate
Saturated Polyester
PEEK
Polyurethane
Some are thermosets as well.
PVC
Not Cross-Linked
90% of market
Thermoplastics
Will reform when melted
Epoxy
Melamine Formaldehyde
Phenolic
Polyester (unsaturated)
Polyimide
Some are thermoplastic as well.
Silicone
Urea Formaldehyde
Cross-linked
10% of market
Thermosets/Elastomers
Will not reform
Polymer Family Tree

8. Ballpark Comparisons Tensile strengths Polymers: ~ 10 - 100 MPa
Metals: 100’s ’s MPa
Elongation
Polymers: up to 1000 % in some cases
Metals: < 100%
Moduli (Elastic or Young’s)
Polymers: ~ 10 MPa - 4 GPa
Metals: ~ GPa

9. Amorphous v Crystalline Polymers Thermo-mechanical properties

10. Thermal Expansion
If a part is to be produced within a close dimensional tolerance, careful consideration of thermal expansion/contraction must be made.
Parts are produced in the melt state, and solidify to amorphous or semi-crystalline states.
Changes in density must
be taken into account
when designing the mold.

11. Thermal Expansion

12. Stress Strain Studies

13. Anatomy of a Stress Strain Graph
Elongation = 100% x  
Initial slope is the Young’s Modulus (E’ or sometimes G)
TS = tensile strength
y = yield strength
Toughness = Energy required to break (area under curve)

14. Compression and Shear vs. Tensile Tests
Stress-strain curves are very dependent on the test method. A modulus determined under compression is generally higher than one derived from a tensile experiment, as shown below for polystyrene.
Tensile testing is most sensitive
to material flaws and microscopic
cracks.
Compression tests tend to
be characteristic of the polymer,
while tension tests are more
characteristic of sample flaws.
Note also that flexural and shear
test modes are commonly
employed.

15. Stress Strain Graphs  
Chains in neck align along elongation direction: strengthening 
Elongation by extension of neck 

16. Beyond “B”, the yield strength, deformations are plastic

17. Ductility & Elongation (EL)
EL < 5% Brittle
EL > 5% Ductile
Thermosets = strong & brittle
Not Ductile
Thermolastics = depends on T

18. Cold Drawing above the Tg

19. TENSILE RESPONSE: • Compare to responses of other polymers:
Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from Fig , Callister 6e. (Fig is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)
• Compare to responses of other polymers:
--brittle response (aligned, cross linked & networked case)
--plastic response (semi-crystalline case) 25

20. Elastomer Molecules High entropy Low entropy Low energy High energy
Model of long elastomer molecules, with low degree of cross‑linking: (a) unstretched, and (b) under tensile stress.
Low entropy
Low energy
High energy

22. YOUNG’S MODULI: COMPARISON
Graphite
Ceramics
Semicond
Metals
Alloys
Composites
/fibers
Polymers
E(GPa)
Based on data in Table B2,
Callister 6e.
Composite data based on
reinforced epoxy with 60 vol%
of aligned
carbon (CFRE),
aramid (AFRE), or
glass (GFRE)
fibers. 13

24. Linear Elasticity: Possion Effect
• Hooke's Law:  = E 
• Poisson's ratio, :
metals:  ~ 0.33
ceramics: ~0.25
polymers: ~0.40
Units:
E: [GPa] or [psi]
n: dimensionless
Why does  have minus sign?

25. Poisson Ratio • Poisson Ratio has a range –1    1/2
Look at extremes
No change in aspect ratio:
Volume (V = AL) remains constant: V =0.
Hence, V = (L A+A L) = So,
In terms of width, A = w2, then A/A = 2 w w/w2 = 2w/w = –L/L.
Hence,
Incompressible solid.
Water (almost).

26. Poisson Ratio: materials specific
Metals: Ir W Ni Cu Al Ag Au
generic value ~ 1/3
Solid Argon: 0.25
Covalent Solids: Si Ge Al2O3 TiC
generic value ~ 1/4
Ionic Solids: MgO 0.19
Silica Glass: 0.20
Polymers: Network (Bakelite) Chain (PE) 0.40
Elastomer: Hard Rubber (Ebonite) (Natural) 0.49

27. Example: Poisson Effect
Tensile stress is applied along cylindrical brass rod (10 mm diameter). Poisson ratio is  = 0.34 and E = 97 GPa.
Determine load needed for 2.5x10–3 mm change in diameter if the deformation is entirely elastic?
Width strain: (note reduction in diameter)
x= d/d = –(2.5x10–3 mm)/(10 mm) = –2.5x10–4
Axial strain: Given Poisson ratio
z= –x/ = –(–2.5x10–4)/0.34 = +7.35x10–4
Axial Stress: z = Ez = (97x103 MPa)(7.35x10–4) = 71.3 MPa.
Required Load: F = zA0 = (71.3 MPa)(5 mm)2 = 5600 N.

29. Negtive poisson’s ratio
foams

30. Compression
Radial
n = -1.24
Axial
n = 0
Lakes, R. S., "No contractile obligations", Nature, 1992, 358,

31. Anisotropic Materials
1) Compaction of UHMWPE powder
2) Sintering
3) Extrusion

32. Mechanical properties are sensitive to temperature
FIGURE Effect of temperature on the stress-strain curve for cellulose acetate, a thermoplastic. Note the large drop in strength and increase in ductility with a relatively small increase in temperature. Source: After T.S. Carswell and H.K. Nason. Manufacturing Processes for Engineering Materials, 5th ed. Kalpakjian • Schmid Prentice Hall,

33. Poly(methyl methacrylate)

34. Lower elastic modulus, yield and ultimate properties
Stress
Strain
Polymers
Metals
Ceramics
Lower elastic modulus, yield and ultimate properties
Greater post-yield deformability
Greater failure strain

36. Polymers: Thermal Properties
In the liquid/melt state enough thermal energy for random motion (Brownian motion) of chains
Motions decrease as the melt is cooled
Motion ceases at “glass transition temperature”
Polymer hard and glassy below Tg, rubbery above Tg

37. Polymers: Thermal PropertiesTg Tm
semicrystalline
log(Modulus)
crosslinked
linear amorphous
Temperature

38. Polymers: Thermal Properties
Stress
Strain
decreasing temperature or increasing crystallinity

39. Properties depend on amount of cross-linking
Increasing cross-linking
Figure M. P. Groover, “Fundamentals of Modern Manufacturing 3/e” John Wiley, 2007

42. Phase diagram for semi-crystalline polymer

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

45. Differential Scanning Calorimetry (DSC)

46. Modulus versus temperature

47. Viscous Response of Newtonian Liquids
The top plane moves at a constant velocity, v, in response to a shear stress: v A y F Dx
There is a velocity gradient (v/y) normal to the area. The viscosity h relates the shear stress, ss, to the velocity gradient.
h 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
The viscosity can thus be seen to relate the shear stress to the shear rate:

48. Measuring viscosities
1 pascal second = 10 poise = 1,000 millipascal second
10-100,000 cP
Requires standards

50. Viscosity of Polymer Melts
Shear thinning behaviour
For comparison: h for water is 10-3 Pa s at room temperature.
Poly(butylene terephthalate) at 285 ºC

51. h ~ tTGP Scaling of Viscosity: h ~ N3.4 h ~ N3.4 N0 ~ N3.4 Why? 3.4
Data shifted for clarity!
3.4
h ~ tTGP
Viscosity is shear-strain rate dependent. Usually measure in the limit of a low shear rate: ho
h ~ N3.4 N0 ~ N3.4
Universal behaviour for linear polymer melts
Applies for higher N: N>NC
Why?
G.Strobl, The Physics of Polymers, p. 221

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

53. 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 tT), creating a “transient” network.

55. 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.

56. “Memory” of Previous State
Poly(styrene)
Tg ~ 100 °C

57. Development of Reptation Scaling Theory
Pierre de Gennes (Paris) developed the concept of polymer reptation and derived scaling relationships.
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.

58. Scaling Concepts in Polymer Physics Cornell University Press, 1979
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
de Gennes
P.G. de Gennes
Scaling Concepts in Polymer Physics
Cornell University Press, 1979

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

60. Amorphous Glasses (< Tg)
This is a self siphoning gel. Add a dispersant such as alcohol to separate the resin particles inhibiting the formation of large insoluble lumps. Any water soluble alcohol can be used as long as it is dry. Mix ml of the alcohol with 3 to 4 grams of polyethylene oxide in a clean dry 600-ml beaker. Swirl the mixture to completely wet the resin with alcohol. Add ml of tap water into the mixture “in one pour” and stir until the resin has gelled completely. Pour the gel into a second 600-ml beaker and then back and forth between the two beakers. The gel can be made to siphon by raising one beaker above the other while gradually pouring the gel. Once the gel starts to pull, separate the two beakers and turn the upper vessel vertically. The gel will move up the sidesw of the beaker as a thin film which forms thick strands as it falls. This process can be continued indefinitely. Add 100 ml of water to the empty beaker and swirl to wet the sides. Pour the gel into the water and then back into the original container. The siphoning process speeds up considerably pulling the gel quickly out of the upper beaker. (Even small strands can start the siphoning process emptying the beaker unexpectedly. The gel can be disposed of in the waste paper basket, it’s 99% water. The glassware can be rinsed with plenty of tap water and dried.
Tg: 40 carbons in backbone
Starting moving in concert

61. Glass transition temperature

62. Rate of cooling affects Tg

63. Polymer
Tg ( °C)

64. Polymer
Tg ( °C)

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

66. Factors that affect Tg
Other polar vinyl polymer:

67. Factors that affect Tg

68. Factors that affect Tg
Main chain stiffness: reduced flexibility

69. Polyarylenes

70. Nylons or polyamides

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

72. Long chains plasticize movements

73. Factors that affect Tg
poly(methyl methacrylate)

74. Factors that affect Tg
Tacticity

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

76. Factors that affect Tg: Mw

77. Factors that affect Tg: Crosslinking

78. Factors that affect Tg: Plasticizer
Phthalates

79. Immiscible (Two phase) and miscible (blends) polymers

80. Tg as a function of film thickness

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

83. Additional Kinds of Transitions

84. Amorphous Polymers Thermo-mechanical properties

85. Crystallinity in Polymers
Maltese cross spherulites
Sheaf-like arrangement of lamellae in a blend of polyethylenes
System: Polyethylene (PE),
Composition: LPE:BPE 3:1
An image of an alkane crystal taken by AFM
System: Alkane, Composition: C36H74
An image of a single crystal alkane
System: Alkane, Composition: C294H590
Single PE spherulite AFM

87. Thermodynamics of melting and crystallization: First order transitions

88. Amorphous v Crystalline Polymers Thermo-mechanical properties

89. Low density polyethylene (LDPE) 915-929 45-65
Medium density polyethylene (MDPE)
High density polyethylene (HDPE)
Material Density (kg/m3) % Crystallinity
Shrinkage, Stiffness, Tensile strength, Hardness, Heat deflection, Chemical resistance
Density Increase
Property
Impact strength, Ductility
Weatherability

90. Thermal Transition Points of Select Polymers

91. Rule of Thumb for Tg’s and Tm’s
For symmetrical polymers: Tg = 0.5 Tm (Kelvin)
Polyvinylidene chloride Tg = = 255 K
Tm = Tg/0.50 = 255/0.5 = 510 K or 237°C
Experimentally Tm = 200 °C
For asymmetrical polymers: Tg = 0.66 Tm (Kelvin)
Polyvinyl chloride Tg = = 377 K
Tm = Tg/0.66 = 354/0.66 = 536 K or 263°C
Experimentally Tm = 273 °C

92. Rule of Thumb for Tg’s and Tm’s
Caution: Its just a rule of thumb:
Atactic polystyrene Tg = = 377 K
Tm = Tg/0.66 = 377/0.66 = 571 K or 298 °C
Experimentally Tm = 523 K or 250 °C

93. Crystalline Polymers (really semicrystalline)
Polar functionality

94. Thermodynamic of Crystallization
For melting Sf is positive

95. Intramolecular interactions (Hf) favor crystallization & higher Tm
Van der Waals:
2 kJ/mole
Hydrogen bonding
20 kJ/mol

96. Explain why Nylon 6 has a lower Tm than Kevlar

97. Entropic Contributions to Tm

98. Flexible Chains have numerous conformations
Nylon 6

99. Rigid Chains have fewer conformations
Kevlar example

101. Polymer symmetry and Melting Point

102. Molecular Weight Influence on Tm
Melting temperatures of n-alkanes (up to C100) as a function of chain length.

103. Methods for Inducing Crystallization in Polymers
Slow cooling of molten polymer
Annealing between Tg and Tm
Evaporation of solvent
Shear & disintanglement
Stretching and alignment of macromolecules

104. Characterization of Crystalline Polymers: Diffraction

105. Rare to get single crystals: Powder XRD or films

106. Polyethylene’s Orthorhombic Unit cell

107. Vinyl Polymer Crystals: Substituents favor helical conformation

108. Characterization of Crystallinity in Polymers
Polymers generally have crystalline and amorphous contributions

109. Lamellar Structure of Polymer crystals

110. Polymer single crystals: Graduate students nightmare
Still lamellar structures

112. Validation of Models

113. Dislocations in Polymer Crystals

114. From singhle crystals to Aggregate structures

115. Polyethylene Spherulites

116. Spherulite Growth from Lamellar crystals

117. Crystalline structures in polymers
TEM of spherulite structure in natural rubber(x30,000).
Chain-folded lamellar crystallites (white lines) ~10nm thick extend radially.

118. • % Crystallinity: % of material that is crystalline.
--TS and E often increase
with % crystallinity.
--Annealing causes
crystalline regions to grow.
% crystallinity increases.

119. Tensile Response: Brittle & Plastic
Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along plastic response curve (purple) adapted from Fig , Callister 6e.

120. Amorphous polymer properties do not depend on cooling rate.
Semicrystalline polymer properties depend on final degree of crystallinity, and hence the rate of cooling.
Lower % S-Cryst
Temperature Tg E
Achieved using slower cooling rates.
Higher % S-Cryst
Cooling rates for semi-crystallines are important!

121. Micrographs of Polymer Spherultes

122. Seeing Maltese Crosses: Polarizing Microscopy

123. Polarizing Optical Microscopy

124. Formation of Ring Pattern: Lamellar Twisting

125. Microfibriallar Morphology

126. Polyethylene Fibers Nucleated on Si-C fibers: Shish-Kebobs

127. Branching on Crystallinity
Which one will be more likely to crystallize?

128. Linear crystallizes easier
(HDPE = linear; LDPE = branched)

130. Nucleation Rates between Tg and Tm

131. Primary Crystallization

132. Quenching Slow Cooling Crystallinity (%) Cooling rate (oC/s) 40 30 2010
0.01
0.1
1.0 10
100
Cooling rate (oC/s)

133. Early stages of crystallation of PEEK in the presence of a carbon fibre.

134. Effects of Crystallinity
Strength: Stronger & Stiffer
Optical: Opaque (scattering by spherulites)
Higher density
Less Soluble
Less Permeable
Smaller interchain distances
Stronger intermolecular forces