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author date title tags uuid lecture_slides exercise_sheets
Akbar Rahman \today MMME2045 // Polymers (Block P)
uni
mmme2045
polymers
22ccabd9-2c10-454c-bf78-cf14c6f96b47
./lectures_slides/MMME2045 UNUK BlockP Part 1.pptx
./lectures_slides/MMME2045 UNUK BlockP Part 2.pptx
./lectures_slides/MMME2045 UNUK BlockP Part 3.pptx
./lectures_slides/MMME2045 UNUK BlockP Part 4.pptx
./lectures_slides/MMME2045 UNUK BlockP Revision and Examples.pptx
./questions/Extra Polymer Questions PQ 5-8.pptx

I don't think I ever finished these notes.

Introduction

  • polymers make up a huge range of products in various fields like electricals, packaging, transport, and more
  • they tend to be light, corrosion resistant and low friction

Case Study: Low Pressure Gas Distribution

national scale transmission:

  • the National Transmission System (NTS), which is operated by the National Grid, has:

    • 7600 km of large diameter steel pipelines (ranging from 63 mm to 1200 mm)
    • 20 compressor stations

  • gas is transported from terminals to 120 offtake installations at 85 bar

    • 8 regional domestic transmission systems
    • 40 large scale industrial consumers, like power stations, at 25 bar
    • 8 large scale storage sites (9 more planned)

regional distribution:

  • 275000 km of small diameter pipes
  • pressure is reduced in stages before reaching residential consumers
  • volume of gas flowing in pipleline network acts as buffer storage, called linepack

Low Pressure Gas Distribution Pipes

Scale Pressure (bar) Priority Material(s) used
national distribution 85 Max flow high speed steel
local distribution 0.075 to 2 \phantom cast iron, PE
inside house < 0.07 Safe and durable copper, lead
laboratory < 0.07 Flexible, easy to change rubber, PVC

  • cast iron used to be used for low pressure distribution until 50s

  • typically 12 foot sections connected by bell and spigot joints

  • sealed by jute fabric and cement or molten lead

  • leaks tend to develop in packing due to overhead traffic, freeze-thaw cycles, shifting soil, and shift to dryer natural gas

  • key problems with cast iron are

    • corrosion
    • brittleness
    • leakage

  • polymer replacements started in 70s and are ongoing

  • but methane leaks through PE

Desirable Properties for Pipes

  • chemical stability
  • toughness, high yield strength
  • stiffness
  • ease of joining
  • pressure requirements
  • low creep
  • high strength
  • minimal runaway crack growth
  • low cost

Design against Creep

  • radial stress tends to be negligble
\epsilon_\theta = \frac{pR}{tE}\left(1-\frac\nu2\right)
\epsilon_\theta = \sigma_\theta J(t)\left(1 - \frac\nu2\right)

creep compliance:

J(t) = \frac{\epsilon(t)}{\sigma}

Selection Criteria for Polymers

Ductility Factor (Critical Crack Length, a_c)

M = \frac{K_{Ic}}{\sigma_y}

critical crack length is when the cracked structure will fail

a_c < \frac1\pi\left(\frac{K_{Ic}}{\sigma_y}\right)^2

where a_c is critical crack length, \sigma_y is yield strength, and K_{Ic} is the plane strain fracture toughness

K_{Ic} = Y\sigma(\pi a)^{\frac12}

where Y is the geometry factor (affected by shape of structure), a is the length of the crack, and \sigma is applied tensile stress

Influence of the Material's Structure

Polyethylene (PE)

  • PE is the simplest polymer, with the chemical formula (C_2H_4)_n, where n is a large number
  • PE is compact and tightly packed making it insensitive to solvents
  • PE has low polarity, making it a good conductor
  • above T_g the C-C bonds can rotate freely allowing chains to form random coils of amorphous regions

Types of PE

  • low density (LDPE) --- density of 915 to 925 kg per cubic meter

    • processed under high pressure (1 to 2 kbar) and high temps (100 to 300 C)
    • very branched molecules (low crystallinity (40 to 60%))
    • T_m \approx 110 C
    • T_g \approx -120 C
    • applications include films, bags, transparent parts, packaging, bubble wrap, flexible caps

  • high density (HDPE) --- density of 945 to 960 kg per cubic meter

    • processed with active catalyst at lower pressure (30 bar) and lower temperature (40 to 150 C)
    • long linear branched molecules (high crystallinity (85 to 95%))
    • applications include pipes pails, covers, chemical containers jars, tanks

  • linear low density (LLDPE) --- same density as LDPE

    • processed at lower temps than LDPE
    • mostly linear polymer with significant numbers of short branches
    • commonly made by copolymerisation of ethylene with short chains of alpha-olefins (e.g. 1-butene, 1-hexene, 1-oxtene)
    • advantages include higher tensile strength, impact and puncture resistance than LDPE, lower thickness films can be blown with environmental stress cracking resistance
    • applications include packaging, bags, cable covering, toys, lids, buckets, containers, pipe

  • medium density (MDPE) --- 926 to 940 kg per cubic metre

    • processed by mechanically mixing LDPE and HDPE
    • has properties of a mix of the two
    • alternatively can be catalysed by catalysts such as chromium and silica
    • applications include water and gas pipes (high shock and drop resistance), sacks, shrink film, packaging film, carrier bags

  • ulta high molecular weight (UHMWPE) --- density of 930 to 940 kg per cubic meter

    • high molar mass of around 3 to 6 million
    • gives it high toughness but difficult to form crystal structure (45% crystallinity)
    • high molecular mass means the long molecules produce more intercrystalline links which increase yield stress through orientation hardening
    • improved abrasion and chemical resistance, resistance to impact, and cyclical failure
    • melt flow index is low and cannot be conventionally injection moulded, blow moulded, or extruded
    • had to be processed by compression moulding or machined
    • applications include bearing surfaces in biomedical implants, marine barriers, rods, pumps, bearings, gaskets

Lamellae

  • PE molecules can also assume a rod like shape and a more crystalline structure
  • PE contains large numbers of heterogenous nuclei (e.g. from catalyst residues)
  • on cooling from melt, lamellae crystals grow from edges of crystal plates so it expands to seveal micrometers while thickness is about 10 to 15 nanometres
  • lamellae form next to it at a slightly different angle and form a funny shape (p7 of [lecture notes](./lecture_notes/BLOCKP Lecture Notes 20-21.pdf)

Semi and Non Crystalline Polymers

  • semicrystalline---polymer crystals are always separated from each other by amorphous layers

  • non-crysalline (amorphous)---glassy polymers, like polystyrene, PMMA, and polycarbonate are known for transparency

    elastomers or rubbers like polyisoprene or butyl rubber are often filled with particles to increase stiffness and reduce wear, making them opaque

Processing of Polymers

Melt Flow Index (MFI)

MFI is the output in grams when 2.16 kg is used to extrude a polymer using these exact dimensions:

Stuff

P = \text{shear stress} \times \text{shear strain}

\Delta P is absolute pressure ?? i think (1:12:00 https://echo360.org.uk/lesson/3c72949d-b5d0-4ffe-b068-9ff663cc4763/classroom#sortDirection=desc)