mmme2045 add incomplete notes on polymers
This commit is contained in:
parent
ec195bbe66
commit
044a898557
GPG Key ID:
20609519444A1269
199
uni/mmme/2045_materials_in_design/polymers.md
Executable file
199
uni/mmme/2045_materials_in_design/polymers.md
Executable file
@ -0,0 +1,199 @@
|
||||
---
|
||||
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 (<http://www.gridwatch.templar.co.uk/>, <https://grid.iamkate.com/>)
|
||||
|
||||
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>)
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user