Exercises: Structure, properties and applications

Polyethylene can be synthesised with different degrees of branching in its macromolecular chains, giving rise to high-density polyethylene ($\mathrm{PEAD}$, density $0.95\,\text{g}\times\text{cm}^{-3}$, melting temperature $132\,{^\circ}\text{C}$) and low-density polyethylene ($\mathrm{PEBD}$, density $0.92\,\text{g}\times\text{cm}^{-3}$, melting temperature $110\,{^\circ}\text{C}$).

1. a) Justify the difference in density observed between the two materials in terms of the spatial structure of their chains.
2. b) Explain, with reasoning, why $\mathrm{PEAD}$ has a significantly higher melting temperature than $\mathrm{PEBD}$.

In the field of sustainable materials chemistry, there is often confusion between the terms "bio-based" and "biodegradable". Consider two commercial polymers: poly(ethylene terephthalate) synthesised from sugar cane bioethanol ($\mathrm{bio\text{-}PET}$) and the petrochemical-origin poly(butylene adipate-co-terephthalate) ($\mathrm{PBAT}$).

1. a) Explain why the origin of a polymer's monomers does not guarantee its biodegradability in the environment, applying the concept to the structure of $\mathrm{bio\text{-}PET}$.
2. b) Justify whether a polymer of entirely petrochemical synthesis, such as $\mathrm{PBAT}$, can legitimately be classified as biodegradable.

Natural rubber consists mainly of poly($\text{cis}$-$1.4$-isoprene). In its raw state it can undergo irreversible flow when heated and change its properties when cooled; these changes depend on temperature, time and crystallinity. To stabilise its mechanical properties against thermal variations, it is subjected to a vulcanisation process with sulfur.

1. a) Describe the structural modification that the material undergoes after reaction with sulfur, in terms of inter-chain bonds.
2. b) Explain why vulcanised rubber retains its elasticity after being deformed and does not flow irreversibly when heated to $100\,{^\circ}\text{C}$.

The thermal and mechanical response of macromolecular materials depends critically on the presence and density of covalent links between their chains. The following diagram illustrates three representative structural arrangements at the macromolecular scale.

1. a) Compare the response of structures A and B when they are subjected to a controlled increase in temperature until the softening zone of material A is exceeded, before its chemical degradation, explaining whether mechanical recycling by melting is possible in each case.
2. b) Explain which structural phenomenon allows network C to recover its initial dimension after withstanding a tensile deformation of $200\,\%$, and state why structure B fractures without undergoing such elastic deformation.

In the synthesis of an absorbable surgical thread, the use of poly(lactic acid) ($\mathrm{PLA}$) is being evaluated. The polymer can be formulated as stereoregular poly($\mathrm{L}$-lactic acid) ($\mathrm{PLLA}$, crystallinity of $45\,\%$, elastic modulus of $3.8\,\text{GPa}$) or as atactic racemic poly($\mathrm{D,L}$-lactic acid) ($\mathrm{PDLLA}$, amorphous, elastic modulus of $1.9\,\text{GPa}$).

1. a) Justify at the macromolecular level why $\mathrm{PLLA}$ is crystalline whereas $\mathrm{PDLLA}$ is completely amorphous.
2. b) When implanted in the body at $37\,{^\circ}\text{C}$ in isotonic saline solution, the mass of the $\mathrm{PDLLA}$ implant decreases by $50\,\%$ after $8\text{ semanas}$, whereas $\mathrm{PLLA}$ requires more than $40\text{ semanas}$ to lose the same percentage. Formulate, with reasoning, a kinetic hypothesis based on water penetration and the accessibility of the ester bond in both matrices.

The synthesis of an epoxy resin for encapsulating electronic circuits is analysed. A linear diepoxide prepolymer is mixed with an aliphatic diamine as a crosslinking agent. At room temperature ($25\,{^\circ}\text{C}$), the mixture initially has a low viscosity, but after heating at $80\,{^\circ}\text{C}$ for $60\text{ minutos}$ a hard, infusible solid forms.

1. a) Identify the type of chemical reaction involved between the oxirane (epoxide) ring and the amino group ($-\mathrm{NH}_2$), and justify why a tetrafunctional diamine (two active protons on each nitrogen) induces the formation of an insoluble three-dimensional network.
2. b) If a monofunctional secondary monoamine, $\mathrm{R_2NH}$, with only one reactive hydrogen, is accidentally added instead of the diamine in the same stoichiometric proportion, explain how the possibility of obtaining separate chains or small molecules soluble in a compatible solvent would change, compared with a covalent network.

A team of materials engineers must select the optimal polymer for manufacturing fluid-conducting pipes in a chemical plant. The fluid flows at $75\,{^\circ}\text{C}$ and contains non-polar hydrocarbons. The candidate materials and their properties tested at $23\,{^\circ}\text{C}$ and at $80\,{^\circ}\text{C}$ are shown in the table:

Polymer	Tg (°C)	Tm (°C)	Modulus at 80 °C (MPa)	Swelling in hexane (% w/w)
PS	100	—	45	68
UHMWPE	−120	135	420	4
PA 6.6	50	260	310	0.8
Crosslinked silicone	−125	—	1.2	82

1. a) Evaluate the suitability of $\mathrm{PS}$ and of silicone rubber for this application, considering the mechanical conditions and solvent resistance.
2. b) Compare $\mathrm{UHMWPE}$ and $\mathrm{PA\text{-}6.6}$, justifying which of them offers more reliable chemical behaviour towards the hydrocarbon fluid, and argue the role of the glass transition temperature ($T_g$) of $\mathrm{PA\text{-}6.6}$ in the stiffness at $80\,{^\circ}\text{C}$. These are teaching data for the grades tested, not universal values. PS: polystyrene; UHMWPE: ultra-high-molecular-weight polyethylene; PA 6.6: polyamide 6,6. Tg indicates the glass transition and Tm the melting; — means the absence of a well-defined crystalline melting point.

To select a biopolymer for packaging fresh food that is sensitive to moisture and oxygen, extruded films of poly(lactic acid) ($\mathrm{PLA}$) and of poly(hydroxybutyrate-co-hydroxyvalerate) ($\mathrm{PHBV}$) are tested.

1. a) The water vapour permeability ($WVP$, in $10^{-11}\,\text{g}\times\text{m}^{-1}\times\text{s}^{-1}\times\text{Pa}^{-1}$) and the oxygen permeability ($OP$, in $10^{-15}\,\text{cm}^3\times\text{m}^{-1}\times\text{s}^{-1}\times\text{Pa}^{-1}$) are measured for three film thicknesses ($25\,\mu\text{m}$, $50\,\mu\text{m}$ and $100\,\mu\text{m}$) at $23\,{^\circ}\text{C}$ and $50\,\%$ relative humidity. It is observed that the permeability coefficient does not vary with thickness, but the total mass flux transmitted per unit time and area is halved when the thickness is doubled. Justify this physico-chemical behaviour using Fick's law of diffusion.
2. b) At $50\,\mu\text{m}$, $\mathrm{PLA}$ has $WVP = 2.4$ and $OP = 3.1$, whereas $\mathrm{PHBV}$ has $WVP = 0.6$ and $OP = 1.2$ in the units indicated. Justify the lower permeability of $\mathrm{PHBV}$ on the basis of its percentage crystallinity ($60\,\%$ in $\mathrm{PHBV}$ compared with $15\,\%$ in the $\mathrm{PLA}$ tested) and the chemical nature of its monomers. Use the steady-state model $J=P\,\Delta p/e$, where $J$ is the flux per unit area, $P$ the permeability, $\Delta p$ the partial pressure difference and $e$ the thickness. Both materials are polyesters; in the PHBV grade tested there is a higher proportion of non-polar aliphatic segments. Formulate a hypothesis consistent with the data, without attributing exclusive causality to a single factor.

An experiment is designed to quantify the viscous creep deformation ("creep") of rectangular specimens ($150\,\text{mm} \times 10\,\text{mm} \times 4\,\text{mm}$) of two engineering thermoplastics: poly(oxymethylene) homopolymer ($\mathrm{POM\text{-}H}$) and poly(oxymethylene) copolymer with dioxolane ($\mathrm{POM\text{-}C}$).

1. a) Design a rigorous experimental protocol to measure the relative deformation as a function of time over $1000\text{ horas}$, stating the variables that must be kept strictly constant (control of load, temperature and dimensions) and the recommended data acquisition frequency.
2. b) At $60\,{^\circ}\text{C}$ and under a constant tensile stress of $15\,\text{MPa}$, the $\mathrm{POM\text{-}H}$ specimen undergoes a final deformation of $1.8\,\%$, whereas the $\mathrm{POM\text{-}C}$ specimen reaches $2.7\,\%$. Given that $\mathrm{POM\text{-}H}$ has a crystallinity of $72\,\%$ and $\mathrm{POM\text{-}C}$ of $60\,\%$, explain at the molecular level how the dioxolane comonomer alters the regularity of the chain and increases creep under continuous load at elevated temperature.