Micro Structures in Polymers - Plastics and Polymers - Lecture Slides, Slides of Mathematical Methods for Numerical Analysis and Optimization

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Micro Structures in Polymers

Chapter 3

Chapter 3 Objectives

• Objectives

• Polymer length, molecular weight, molecular weight

distribution (MWD)

• Physical and mechanical property implications of

molecular weight and MWD

• Melt Index
• Amorphous and crystalline structures in polymers
• Thermal transitions in plastics (thermoplastics and

thermosets

• Steric (shape) effects

Molecular Weight

• Average Molecular Weight

• Polymers are made up of many molecular weights or a

distribution of chain lengths.

• The polymer is comprised of a bag of worms of the same repeating unit, ethylene (C 2 H 4 ) with different lengths; some longer than others.
• Example,
  • Polyethylene -(C 2 H 4 )- 1000 has some chains (worms) with 1001 repeating ethylene units, some with 1010 ethylene units, some with 999 repeating units, and some with 990 repeating units.
  • The average number of repeating units or chain length is 1000 repeating ethylene units for a molecular weight of 28*1000 or 28, g/mole.

Molecular Weight

• Average Molecular Weight

• Distribution of values is useful statistical way to

characterize polymers.

• For example,
  • Value could be the heights of students in a room.
  • Distribution is determined by counting the number of students in the class of each height.
  • The distribution can be visualized by plotting the number of students on the x-axis and the various heights on the y-axis.

5

Histogram of Heights of Students

0

(^105)

1520

25

60 70 80 Height, inches

Frequency

Series

Molecular Weight

• Average Molecular Weight

• Determined by summing the weights of all of the chains

and then dividing by the total number of chains.

• Average molecular weight is an important method of

characterizing polymers.

• 3 ways to represent Average molecular weight
  • Number average molecular weight
  • Weight average molecular weight
  • Z-average molecular weight

Gel Permeation Chromatography

• GPC Used to measure Molecular Weights

• form of size-exclusion chromatography
• smallest molecules pass through bead pores, resulting in

a relatively long flow path

• largest molecules flow around beads, resulting in a

relatively short flow path

• chromatogram obtained shows intensity vs. elution

volume

• correct pore sizes and solvent critical

Number Average Molecular Weight, Mn

• where Mi is the molecular weight of that species (on the x-axis)
• where Ni is the number of molecules of a particular molecular species I (on the y-axis).
• Number Average Molecular Weight gives the same weight to all polymer lengths, long and short.
• Example, What is the molecular weight of a polymer sample in which the polymers molecules are divided into 5 categories.
• Group Frequency
• 50,000 1
• 100,000 4
• 200,000 5
• 500,000 3
• 700,000 1

10

1 2 3

1 1 2 2 3 3

∑

∑ N N N

N M N M N M

N

N M

M

i

i i n

260 , 000

( 1 4 5 3 1 )

1 ( 50 ) 4 ( 100 ) 5 ( 200 ) 3 ( 500 ) 1 ( 700 )

...

... 1 2 3

1 1 2 2 3 3

=

= + + + +

= = + + +

n

n

i n i i

M

M K K K K K

N N N

N M N M N M N M N M

Molecular Weight

• Number Average Molecular Weight. Figure 3.

• The data yields a nonsymmetrical curve (common)
• The curve is skewed with a tail towards the high MW
• The Mn is determined experimentally by analyzing the

number of end groups (which permit the determination of

the number of chains)

• The number of repeating units, n, can be found by the ratio

of the Mn and the molecualr weight of the repeating unit,

M 0 , for example for polyethylene, M 0 = 28 g/mole

• The number of repeating units, n, is often called the degree

of polymerization, DP.

• DP relates the amount of

monomer that has been converted to polymer.

11

M 0

M

n = n

Z- Average Molecular Weight

• Emphasizes large molecules even more than Mw
• Useful for some calculations involving mechanical

properties.

• Method uses a centrifuge to separate the polymer

13

2 3 3

2 2 2

2 1 1

3 3 3

3 2 2

3 1 1 2

3

N M N M N M

N M N M N M

N M

N M

M

i i

i i z

Molecular Weight Distribution

• Molecular Weight Distribution represents the

frequency of the polymer lengths

• The frequency can be Narrow or Broad, Fig 3.

• Narrow distribution represents polymers of about

the same length.

• Broad distribution represents polymers with varying

lengths

• MW distribution is controlled by the conditions

during polymerization

• MW distributions can be symmetrical or skewed.

Physical and Mechanical Property Implications of MW and MWD

• Higher MW increases tensile strength
  • Resistance to an applied load pulling in opposite directions
  • Tension forces cause the polymers to align and reduce the number of entanglements. If the polymer has many entanglements, the force would be greater.
• Broader MW Distribution decreases tensile strength
  • Broad MW distribution represents polymer with many shorter molecules which are not as entangled and slide easily.
• Higher MW increases impact strength
  • Impact toughness or impact strength are increased with longer polymer chains because the energy is transmitted down chain.
• Broader MW Distribution decreases impact strength
  • Shorter chains do not transmit as much energy during impact

Thermal Property Implications of MW & MWD

• Higher MW increases Melting Point
  • Melting point is a measure of the amount of energy necessary to have molecules slide freely past one another.
  • If the polymer has many entanglements, the energy required would be greater.
  • Low molecular weights reduce melting point and increase ease of processing.
• Broader MW Distribution decreases Melting Point
  • Broad MW distribution represents polymer with many shorter molecules which are not as entangled and melt sooner.
  • Broad MW distribution yields an easier processed polymer

17

• Decomposition

Melt Index

• Melt index test measure the ease

of flow for material

• Procedure (Figure 3.6)

• Heat cylinder to desired temperature (melt temp)
• Add plastic pellets to cylinder and pack with rod
• Add test weight or mass to end of rod (5kg)
• Wait for plastic extrudate to flow at constant rate
• Start stop watch (10 minute duration)
• Record amount of resin flowing on pan during time limit
• Repeat as necessary at different temperatures and weights

• Melt index is similar to viscosityMelt Index and Viscosity

• Viscosity is a measure of the materials resistance to flow.
  • Viscosity is measured at several temperatures and shear rates
  • Melt index is measured at one temperature and one weight.
• High melt index = high flow = low viscosity
• Low melt index = slow flow = high viscosity
• Example, (flow in 10 minutes) Polymer Temp Mass
  • HDPE 190C 10kg
  • Nylon 235C 1.0kg
  • PS 200C 5.0Kg