mmme2045 add incomplete notes on polymers
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uni/mmme/2045_materials_in_design/polymers.md
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uni/mmme/2045_materials_in_design/polymers.md
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---
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author: Akbar Rahman
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date: \today
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title: MMME2045 // Polymers (Block P)
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tags: [ uni, mmme2045, polymers ]
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uuid: 22ccabd9-2c10-454c-bf78-cf14c6f96b47
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lecture_slides: [ ./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 ]
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exercise_sheets: [ ./questions/Extra Polymer Questions PQ 5-8.pptx ]
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---
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> I don't think I ever finished these notes.
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# Introduction
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- polymers make up a huge range of products in various fields like electricals, packaging,
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transport, and more
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- they tend to be light, corrosion resistant and low friction
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# Case Study: Low Pressure Gas Distribution
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- the UK currently depends on a lot of gas for its power (<http://www.gridwatch.templar.co.uk/>, <https://grid.iamkate.com/>)
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national scale transmission:
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- the National Transmission System (NTS), which is operated by the National Grid, has:
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- 7600 km of large diameter steel pipelines (ranging from 63 mm to 1200 mm)
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- 20 compressor stations
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- gas is transported from terminals to 120 offtake installations at 85 bar
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- 8 regional domestic transmission systems
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- 40 large scale industrial consumers, like power stations, at 25 bar
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- 8 large scale storage sites (9 more planned)
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regional distribution:
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- 275000 km of small diameter pipes
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- pressure is reduced in stages before reaching residential consumers
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- volume of gas flowing in pipleline network acts as buffer storage, called linepack
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## Low Pressure Gas Distribution Pipes
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Scale | Pressure (bar)| Priority | Material(s) used
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--------------------- | ------------- | ------------------------ | ----------------
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national distribution | 85 | Max flow | high speed steel
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local distribution | 0.075 to 2 | \phantom | cast iron, PE
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inside house | < 0.07 | Safe and durable | copper, lead
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laboratory | < 0.07 | Flexible, easy to change | rubber, PVC
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- cast iron used to be used for low pressure distribution until 50s
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- typically 12 foot sections connected by bell and spigot joints
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- sealed by jute fabric and cement or molten lead
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- leaks tend to develop in packing due to overhead traffic, freeze-thaw cycles, shifting soil, and
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shift to dryer natural gas
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- key problems with cast iron are
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- corrosion
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- brittleness
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- leakage
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- polymer replacements started in 70s and are ongoing
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- but methane leaks through PE
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## Desirable Properties for Pipes
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- chemical stability
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- toughness, high yield strength
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- stiffness
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- ease of joining
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- pressure requirements
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- low creep
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- high strength
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- minimal runaway crack growth
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- low cost
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## Design against Creep
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- radial stress tends to be negligble
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$$\epsilon_\theta = \frac{pR}{tE}\left(1-\frac\nu2\right)$$
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$$\epsilon_\theta = \sigma_\theta J(t)\left(1 - \frac\nu2\right)$$
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### creep compliance:
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$$J(t) = \frac{\epsilon(t)}{\sigma}$$
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# Selection Criteria for Polymers
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## Ductility Factor (Critical Crack Length, $a_c$)
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$$M = \frac{K_{Ic}}{\sigma_y}$$
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critical crack length is when the cracked structure will fail
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$$a_c < \frac1\pi\left(\frac{K_{Ic}}{\sigma_y}\right)^2$$
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where $a_c$ is critical crack length, $\sigma_y$ is yield strength, and $K_{Ic}$ is the plane strain
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fracture toughness
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$$K_{Ic} = Y\sigma(\pi a)^{\frac12}$$
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where $Y$ is the geometry factor (affected by shape of structure), $a$ is the length of the crack,
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and $\sigma$ is applied tensile stress
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# Influence of the Material's Structure
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## Polyethylene (PE)
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- PE is the simplest polymer, with the chemical formula $(C_2H_4)_n$, where $n$ is a large number
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- PE is compact and tightly packed making it insensitive to solvents
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- PE has low polarity, making it a good conductor
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- above $T_g$ the C-C bonds can rotate freely allowing chains to form random coils of amorphous regions
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### Types of PE
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- low density (LDPE) --- density of 915 to 925 kg per cubic meter
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- processed under high pressure (1 to 2 kbar) and high temps (100 to 300 C)
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- very branched molecules (low crystallinity (40 to 60%))
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- $T_m \approx 110$ C
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- $T_g \approx -120$ C
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- applications include films, bags, transparent parts, packaging, bubble wrap, flexible caps
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- high density (HDPE) --- density of 945 to 960 kg per cubic meter
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- processed with active catalyst at lower pressure (30 bar) and lower temperature (40 to 150 C)
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- long linear branched molecules (high crystallinity (85 to 95%))
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- applications include pipes pails, covers, chemical containers jars, tanks
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- linear low density (LLDPE) --- same density as LDPE
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- processed at lower temps than LDPE
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- mostly linear polymer with significant numbers of short branches
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- commonly made by copolymerisation of ethylene with short chains of alpha-olefins (e.g.
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1-butene, 1-hexene, 1-oxtene)
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- advantages include higher tensile strength, impact and puncture resistance than LDPE, lower
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thickness films can be blown with environmental stress cracking resistance
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- applications include packaging, bags, cable covering, toys, lids, buckets, containers, pipe
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- medium density (MDPE) --- 926 to 940 kg per cubic metre
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- processed by mechanically mixing LDPE and HDPE
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- has properties of a mix of the two
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- alternatively can be catalysed by catalysts such as chromium and silica
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- applications include water and gas pipes (high shock and drop resistance), sacks, shrink film,
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packaging film, carrier bags
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- ulta high molecular weight (UHMWPE) --- density of 930 to 940 kg per cubic meter
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- high molar mass of around 3 to 6 million
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- gives it high toughness but difficult to form crystal structure (45% crystallinity)
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- high molecular mass means the long molecules produce more intercrystalline links which
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increase yield stress through orientation hardening
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- improved abrasion and chemical resistance, resistance to impact, and cyclical failure
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- melt flow index is low and cannot be conventionally injection moulded, blow moulded, or
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extruded
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- had to be processed by compression moulding or machined
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- applications include bearing surfaces in biomedical implants, marine barriers, rods, pumps,
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bearings, gaskets
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### Lamellae
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- PE molecules can also assume a rod like shape and a more crystalline structure
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- PE contains large numbers of heterogenous nuclei (e.g. from catalyst residues)
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- on cooling from melt, lamellae crystals grow from edges of crystal plates so it expands to seveal
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micrometers while thickness is about 10 to 15 nanometres
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- lamellae form next to it at a slightly different angle and form a funny shape (p7 of
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[lecture notes](./lecture_notes/BLOCKP Lecture Notes 20-21.pdf)
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## Semi and Non Crystalline Polymers
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- semicrystalline---polymer crystals are always separated from each other by amorphous layers
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- non-crysalline (amorphous)---glassy polymers, like polystyrene, PMMA, and polycarbonate are known
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for transparency
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elastomers or rubbers like polyisoprene or butyl rubber are often filled with particles to
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increase stiffness and reduce wear, making them opaque
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# Processing of Polymers
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## Melt Flow Index (MFI)
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MFI is the output in grams when 2.16 kg is used to extrude a polymer using these exact dimensions:
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# Stuff
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$$P = \text{shear stress} \times \text{shear strain}$$
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$\Delta P$ is absolute pressure ?? i think (1:12:00 <https://echo360.org.uk/lesson/3c72949d-b5d0-4ffe-b068-9ff663cc4763/classroom#sortDirection=desc>)
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