diff --git a/uni/mmme/2045_materials_in_design/polymers.md b/uni/mmme/2045_materials_in_design/polymers.md new file mode 100755 index 0000000..9fd8a7d --- /dev/null +++ b/uni/mmme/2045_materials_in_design/polymers.md @@ -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 (, ) + +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 ) + + +