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+---
+author: Akbar Rahman
+date: \today
+title: MMME2045 // Polymers (Block P)
+tags: [ uni, mmme2045, polymers ]
+uuid: 22ccabd9-2c10-454c-bf78-cf14c6f96b47
+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 ]
+exercise_sheets: [ ./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
+
+- the UK currently depends on a lot of gas for its power (, )
+
+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:
+
+![](./images/vimscrot-2022-11-10T20:50:05,302396063+00:00.png)
+
+# Stuff
+
+$$P = \text{shear stress} \times \text{shear strain}$$
+
+![](./images/vimscrot-2022-11-10T21:01:22,450954684+00:00.png)
+
+$\Delta P$ is absolute pressure ?? i think (1:12:00 )
+
+
+